526 PART 3 • Market Structure and Competitive Strategy b. Suppose that both firms try to maximize profits, b. If each network is risk-averse and uses a maximin but that Firm A has a head start in planning and can strategy, what will be the resulting equilibrium? commit first. Now what will be the outcome? What will be the outcome if Firm B has the head start in c. What will be the equilibrium if Network 1 makes its planning and can commit first? selection first? If Network 2 goes first? c. Getting a head start costs money. (You have to gear d. Suppose the network managers meet to coordinate up a large engineering team.) Now consider the schedules and Network 1 promises to schedule two-stage game in which, first, each firm decides its big show first. Is this promise credible? What how much money to spend to speed up its plan- would be the likely outcome? ning, and, second, it announces which product (H or L) it will produce. Which firm will spend more 6. Two competing firms are each planning to introduce to speed up its planning? How much will it spend? a new product. Each will decide whether to produce Should the other firm spend anything to speed up Product A, Product B, or Product C. They will make its planning? Explain. their choices at the same time. The resulting payoffs are shown below. 4. Two firms are in the chocolate market. Each can choose to go for the high end of the market (high quality) or A A Firm 2 C the low end (low quality). Resulting profits are given B ؊10, ؊10 B 10, 20 by the following payoff matrix: C ؊5, 15 10, 0 0, 10 ؊30, ؊30 Firm 2 Firm 1 20, 10 ؊20, ؊20 Low High 15, ؊5 Low ؊20, ؊30 900, 600 a. Are there any Nash equilibria in pure strategies? If High so, what are they? Firm 1 100, 800 50, 50 b. If both firms use maximin strategies, what outcome a. What outcomes, if any, are Nash equilibria? will result? b. If the managers of both firms are conservative and c. If Firm 1 uses a maximin strategy and Firm 2 knows each follows a maximin strategy, what will be the this, what will Firm 2 do? outcome? c. What is the cooperative outcome? 7. We can think of U.S. and Japanese trade policies as a d. Which firm benefits most from the cooperative out- prisoners’ dilemma. The two countries are consider- come? How much would that firm need to offer the ing policies to open or close their import markets. The other to persuade it to collude? payoff matrix is shown below. 5. Two major networks are competing for viewer rat- ings in the 8:00–9:00 p.m. and 9:00–10:00 p.m. slots Japan on a given weeknight. Each has two shows to fill these time periods and is juggling its lineup. Each Open Close can choose to put its “bigger” show first or to place it second in the 9:00–10:00 p.m. slot. The combination Open 10, 10 5, 5 of decisions leads to the following “ratings points” Close results: U.S. ؊100, 5 1, 1 Network 2 a. Assume that each country knows the payoff matrix and believes that the other country will act in its First Second own interest. Does either country have a dominant strategy? What will be the equilibrium policies if First 20, 30 18, 18 each country acts rationally to maximize its wel- Second fare? Network 1 15, 15 30, 10 b. Now assume that Japan is not certain that the a. Find the Nash equilibria for this game, assuming United States will behave rationally. In particular, that both networks make their decisions at the same Japan is concerned that U.S. politicians may want time. to penalize Japan even if that does not maximize U.S. welfare. How might this concern affect Japan’s choice of strategy? How might this change the equi- librium?
CHAPTER 13 • Game Theory and Competitive Strategy 527 8. You are a duopolist producer of a homogeneous good. the choice of two technologies. Technology A is pub- Both you and your competitor have zero marginal licly available and will result in annual costs of costs. The market demand curve is CA(q) = 10 + 8q P = 30 - Q Technology B is a proprietary technology developed in where Q = Q1 + Q2. Q1 is your output and Q2 your com- Defendo’s research labs. It involves a higher fixed cost petitor’s output. Your competitor has also read this of production but lower marginal costs: book. a. Suppose you will play this game only once. If you CB(q) = 60 + 2q and your competitor must announce your outputs Defendo must decide which technology to adopt. at the same time, how much will you choose to Market demand for the new product is P = 20 Ϫ Q, produce? What do you expect your profit to be? where Q is total industry output. Explain. a. Suppose Defendo were certain that it would main- b. Suppose you are told that you must announce your output before your competitor does. How much tain its monopoly position in the market for the will you produce in this case, and how much do entire product lifespan (about five years) without you think your competitor will produce? What do threat of entry. Which technology would you advise you expect your profit to be? Is announcing first an Defendo to adopt? What would be Defendo’s profit advantage or a disadvantage? Explain briefly. How given this choice? much would you pay for the option of announcing b. Suppose Defendo expects its archrival, Offendo, to either first or second? consider entering the market shortly after Defendo c. Suppose instead that you are to play the first introduces its new product. Offendo will have round of a series of 10 rounds (with the same com- access only to Technology A. If Offendo does enter petitor). In each round, you and your competi- the market, the two firms will play a Cournot game tor announce your outputs at the same time. You (in quantities) and arrive at the Cournot-Nash want to maximize the sum of your profits over equilibrium. the 10 rounds. How much will you produce in the first round? How much do you expect to produce i. If Defendo adopts Technology A and Offendo in the tenth round? In the ninth round? Explain enters the market, what will be the profit of briefly. each firm? Would Offendo choose to enter the d. Once again you will play a series of 10 rounds. market given these profits? This time, however, in each round your competi- tor will announce its output before you announce ii. If Defendo adopts Technology B and Offendo yours. How will your answers to (c) change in this enters the market, what will be the profit of case? each firm? Would Offendo choose to enter the 9. You play the following bargaining game. Player A market given these profits? moves first and makes Player B an offer for the divi- sion of $100. (For example, Player A could suggest iii. Which technology would you advise Defendo that she take $60 and Player B take $40.) Player B can to adopt given the threat of possible entry? accept or reject the offer. If he rejects it, the amount What will be Defendo’s profit given this of money available drops to $90, and he then makes choice? What will be consumer surplus given an offer for the division of this amount. If Player A this choice? rejects this offer, the amount of money drops to $80 and Player A makes an offer for its division. If Player c. What happens to social welfare (the sum of con- B rejects this offer, the amount of money drops to 0. sumer surplus and producer profit) as a result of Both players are rational, fully informed, and want to the threat of entry in this market? What happens maximize their payoffs. Which player will do best in to equilibrium price? What might this imply about this game? the role of potential competition in limiting market *10. Defendo has decided to introduce a revolutionary power? video game. As the first firm in the market, it will have a monopoly position for at least some time. In decid- 11. Three contestants, A, B, and C, each has a balloon and ing what type of manufacturing plant to build, it has a pistol. From fixed positions, they fire at each other’s balloons. When a balloon is hit, its owner is out. When only one balloon remains, its owner gets a $1000 prize. At the outset, the players decide by lot the order in which they will fire, and each player can choose any remaining balloon as his target. Everyone knows that A is the best shot and always hits the target, that B hits
528 PART 3 • Market Structure and Competitive Strategy the target with probability .9, and that C hits the target 13. You are in the market for a new house and have decided with probability .8. Which contestant has the highest to bid for a house at auction. You believe that the value probability of winning the $1000? Explain why. of the house is between $125,000 and $150,000, but 12. An antique dealer regularly buys objects at hometown you are uncertain as to where in the range it might auctions whose bidders are limited to other dealers. be. You do know, however, that the seller has reserved Most of her successful bids turn out to be financially the right to withdraw the house from the market if the worthwhile because she is able to resell the antiques winning bid is not satisfactory. for a profit. On occasion, however, she travels to a a. Should you bid in this auction? Why or why not? nearby town to bid in an auction that is open to the b. Suppose you are a building contractor. You plan public. She often finds that on the rare occasions in to improve the house and then to resell it at a which she does bid successfully, she is disappointed— profit. How does this situation affect your answer the antique cannot be sold at a profit. Can you explain to (a)? Does it depend on the extent to which your the difference in her success between the two sets of skills are uniquely suitable to improving this par- circumstances? ticular house?
C H A P T E R 14 Markets for Factor Inputs So far we have concentrated on output markets: markets for goods CHAPTER OUTLINE and services that firms sell and consumers purchase. In this chapter, we discuss factor markets: markets for labor, raw materi- 14.1 Competitive Factor Markets als, and other inputs to production. Much of our material will be famil- 529 iar because the same forces that shape supply and demand in output markets also affect factor markets. 14.2 Equilibrium in a Competitive Factor Market We have seen that some output markets are perfectly or almost per- 542 fectly competitive, while producers in others have market power. The same is true for factor markets. We will examine three different factor 14.3 Factor Markets with market structures: Monopsony Power 546 1. Perfectly competitive factor markets; 14.4 Factor Markets with 2. Markets in which buyers of factors have monopsony power; Monopoly Power 550 3. Markets in which sellers of factors have monopoly power. LIST OF EXAMPLES We will also point out instances in which equilibrium in the factor market depends on the extent of market power in output markets. 14.1 The Demand for Jet Fuel 536 14.1 Competitive Factor Markets 14.2 Labor Supply for One- and A competitive factor market is one in which there are a large number of Two-Earner Households sellers and buyers of a factor of production, such as labor or raw mate- 541 rials. Because no single seller or buyer can affect the price of a given factor, each is a price taker. For example, if individual firms that buy 14.3 Pay in the Military lumber to construct homes purchase a small share of the total volume 545 of lumber available, their purchasing decision will have no effect on price. Likewise, if each supplier of lumber controls only a small share 14.4 Monopsony Power in the of the market, no individual supplier’s decision will affect the price Market for Baseball Players of the lumber that he sells. Instead, the price of lumber (and the total 548 quantity produced) will be determined by the aggregate supply and demand for lumber. 14.5 Teenage Labor Markets and the Minimum Wage We begin by analyzing the demands for a factor by individual firms. 549 These demands are added to get market demand. We then shift to the supply side of the market and show how market price and input levels 14.6 The Decline of Private-Sector are determined. Unionism 553 14.7 Wage Inequality Revisited 554 529
530 PART 3 • Market Structure and Competitive Strategy • derived demand Demand Demand for a Factor Input When Only for an input that depends on, One Input Is Variable and is derived from, both the firm’s level of output and the Like demand curves for the final goods that result from the production process, cost of inputs. demand curves for factors of production are downward sloping. Unlike con- sumers’ demands for goods and services, however, factor demands are derived • marginal revenue product demands: They depend on, and are derived from, the firm’s level of output and Additional revenue resulting the costs of inputs. For example, the demand of the Microsoft Corporation for from the sale of output created computer programmers is a derived demand that depends not only on the current by the use of one additional unit salaries of programmers, but also on how much software Microsoft expects to sell. of an input. To analyze factor demands, we will use the material from Chapter 7 that Recall that in §8.3, marginal shows how a firm chooses its production inputs. We will assume that the firm revenue is defined to be the produces its output using two inputs, capital K and labor L, that can be hired at increase in revenue resulting the prices r (the rental cost of capital) and w (the wage rate), respectively.1 We from a one-unit increase in will also assume that the firm has its plant and equipment in place (as in a short- output. run analysis) and must only decide how much labor to hire. Suppose that the firm has hired a certain number of workers and wants to know whether it is profitable to hire one additional worker. This will be profit- able if the additional revenue from the output of the worker’s labor is greater than its cost. The additional revenue from an incremental unit of labor, the marginal revenue product of labor, is denoted MRPL. The cost of an incremen- tal unit of labor is the wage rate, w. Thus, it is profitable to hire more labor if the MRPL is at least as large as the wage rate w. How do we measure the MRPL? It’s the additional output obtained from the addi- tional unit of this labor, multiplied by the additional revenue from an extra unit of out- put. The additional output is given by the marginal product of labor MPL and the additional revenue by the marginal revenue MR. Formally, the marginal revenue product is ⌬R/⌬L, where L is the number of units of labor input and R is revenue. The additional output per unit of labor, the MPL, is given by ⌬Q/⌬L, and marginal revenue, MR, is equal to ⌬R/⌬Q. Because ⌬R/⌬L = (⌬R)/(⌬Q)(⌬Q/⌬L), it follows that MRPL = (MR)(MPL) (14.1) In §8.2, we explain that This important result holds for any competitive factor market, whether or because the demand facing not the output market is competitive. However, to examine the characteristics of each firm in a competitive the MRPL, let’s begin with the case of a perfectly competitive output (and input) market is perfectly elastic, market. In a competitive output market, a firm will sell all its output at the mar- each firm will sell its out- ket price P. The marginal revenue from the sale of an additional unit of output put at a price equal to its is then equal to P. In this case, the marginal revenue product of labor is equal to average revenue and to its the marginal product of labor times the price of the product: marginal revenue. MRPL = (MPL)(P) (14.2) In §6.2, we explain the law The higher of the two curves in Figure 14.1 represents the MRPL curve for a of diminishing marginal firm in a competitive output market. Note that because there are diminishing returns—as the use of an marginal returns to labor, the marginal product of labor falls as the amount of input increases with other labor increases. The marginal revenue product curve thus slopes downward, inputs fixed, the resulting even though the price of the output is constant. additions to output will eventually decrease. 1We implicitly assume that all inputs to production are identical in quality. Differences in workers’ skills and abilities are discussed in Chapter 17.
Wage CHAPTER 14 • Markets for Factor Inputs 531 (dollars per Competitive Output Market hour) MRPL ϭ MPL · P Monopolistic Output MRPL ϭ MPL · MR Market Hours of work FIGURE 14.1 MARGINAL REVENUE PRODUCT In a competitive factor market in which the producer is a price taker, the buyer’s demand for an input is given by the marginal revenue product curve. The MRP curve falls because the mar- ginal product of labor falls as hours of work increase. When the producer of the product has monopoly power, the demand for the input is also given by the MRP curve. In this case, how- ever, the MRP curve falls because both the marginal product of labor and marginal revenue fall. The lower curve in Figure 14.1 is the MRPL curve when the firm has monop- oly power in the output market. When firms have monopoly power, they face a downward-sloping demand curve and must therefore lower the price of all units of the product in order to sell more of it. As a result, marginal revenue is always less than price (MR < P). This explains why the monopolistic curve lies below the competitive curve and why marginal revenue falls as output increases. Thus the marginal revenue product curve slopes downward in this case because the marginal revenue curve and the marginal product curve slope downward. Note that the marginal revenue product tells us how much the firm should be willing to pay to hire an additional unit of labor. As long as the MRPL is greater than the wage rate, the firm should hire more labor. If the marginal revenue prod- uct is less than the wage rate, the firm should lay off workers. Only when the marginal revenue product is equal to the wage rate will the firm have hired the profit-maximizing amount of labor. The profit-maximizing condition is therefore MRPL = w (14.3) Figure 14.2 illustrates this condition. The demand for labor curve DL is the MRPL. Note that the quantity of labor demanded increases as the wage rate falls.
532 PART 3 • Market Structure and Competitive Strategy FIGURE 14.2 Price of SL labor HIRING BY A FIRM IN THE LABOR MARKET MRPL ϭ DL (WITH FIXED CAPITAL) w* Quantity of labor In a competitive labor market, a firm faces a perfectly elastic supply of labor SL and can hire as many work- ers as it wants at a wage rate w*. The firm’s demand for labor DL is given by its marginal revenue product of labor MRPL. The profit-maximizing firm will hire L* units of labor at the point where the marginal rev- enue product of labor is equal to the wage rate. L* In §8.3, we explain that a Because the labor market is perfectly competitive, the firm can hire as many firm maximizes its profit by workers as it wants at the market wage w* and is not able to affect the market choosing an output at which wage. The supply of labor curve facing the firm SL is thus a horizontal line. The marginal revenue equals profit-maximizing amount of labor that the firm hires, L*, is at the intersection of marginal cost. the supply and demand curves. Figure 14.3 shows how the quantity of labor demanded changes in response to a drop in the market wage rate from w1 to w2. The wage rate might decrease if more people entering the labor force are looking for jobs for the first time (as happened, for example, when the baby boomers came of age). The quantity of labor demanded by the firm is initially L1, at the intersection of MRPL and S1. Price of labor FIGURE 14.3 w1 S1 w2 S2 A SHIFT IN THE SUPPLY OF LABOR MRPL = DL When the supply of labor facing the firms is S1, the firm hires L1 units of labor at wage w1. But when the Quantity market wage rate decreases and the supply of labor of labor shifts to S2, the firm maximizes its profit by moving along the demand for labor curve until the new wage rate w2 is equal to the marginal revenue product of labor. As a result, L2 units of labor are hired. L1 L2
CHAPTER 14 • Markets for Factor Inputs 533 However, when the supply of labor curve shifts from S1 to S2, the wage falls from w1 to w2 and the quantity of labor demanded increases from L1 to L2. Factor markets are similar to output markets in many ways. For example, the factor market profit-maximizing condition that the marginal revenue product of labor be equal to the wage rate is analogous to the output market condition that marginal revenue be equal to marginal cost. To see why this is true, recall that MRPL = (MPL)(MR) and divide both sides of equation (14.3) by the marginal product of labor. Then, MR = w/MPL (14.4) Because MPL measures additional output per unit of input, the right-hand side of equation (14.4) measures the marginal cost of an additional unit of out- put (the wage rate multiplied by the labor needed to produce one unit of out- put). Equation (14.4) shows that both the hiring and output choices of the firm follow the same rule: Inputs or outputs are chosen so that marginal revenue (from the sale of output) is equal to marginal cost (from the purchase of inputs). This principle holds in both competitive and noncompetitive markets. Demand for a Factor Input When Several Inputs Are Variable When the firm simultaneously chooses quantities of two or more variable inputs, the hiring problem becomes more difficult because a change in the price of one input will change the demand for others. Suppose, for example, that both labor and assembly-line machinery are variable inputs for producing farm equipment. Let’s say that we wish to determine the firm’s demand for labor curve. As the wage rate falls, more labor will be demanded even if the firm’s investment in machinery is unchanged. But as labor becomes less expensive, the marginal cost of producing the farm equipment falls. Consequently, it is profit- able for the firm to increase its output. In that case, the firm is likely to invest in additional machinery to expand production capacity. Expanding the use of machinery causes the marginal revenue product of labor curve to shift to the right; in turn, the quantity of labor demanded increases. Figure 14.4 illustrates this. Suppose that when the wage rate is $20 per hour, the firm hires 100 worker-hours, as shown by point A on the MRPL1 curve. Now consider what happens when the wage rate falls to $15 per hour. Because the marginal revenue product of labor is now greater than the wage rate, the firm will demand more labor. But the MRPL1 curve describes the demand for labor when the use of machinery is fixed. In fact, a greater amount of labor causes the marginal product of capital to rise, which encourages the firm to rent more machinery as well as hire more labor. Because there is more machinery, the mar- ginal product of labor will increase. (With more machinery, workers can be more productive.) The marginal revenue product curve will therefore shift to the right (to MRPL2). Thus, when the wage rate falls, the firm will use 140 hours of labor. This is shown by a new point on the demand curve, C, rather than 120 hours as given by B. A and C are both on the firm’s demand for labor curve (with machin- ery variable) DL; B is not. Note that as constructed, the demand for labor curve is more elastic than either of the two marginal product of labor curves (which presume no change in the amount of machinery). Thus, when capital inputs are variable in the long run, there is a greater elasticity of demand because firms can substitute capital for labor in the production process.
534 PART 3 • Market Structure and Competitive Strategy FIGURE 14.4 Wage A C (dollars per B FIRM’S DEMAND CURVE FOR DL LABOR (WITH VARIABLE CAPITAL) hour) MRPL1 MRPL2 When two or more inputs are variable, 20 a firm’s demand for one input depends 15 on the marginal revenue product of both inputs. When the wage rate is $20, A rep- 10 resents one point on the firm’s demand 5 for labor curve. When the wage rate falls to $15, the marginal product of capital 40 80 120 160 Hours rises, encouraging the firm to rent more of work machinery and hire more labor. As a result, the MRP curve shifts from MRPL1 to MRPL2, generating a new point C on the firm’s demand for labor curve. Thus A and C are on the demand for labor curve, but B is not. Recall from §4.3 that the The Market Demand Curve market demand curve for a product shows how much of When we aggregated the individual demand curves of consumers to obtain the the product consumers are market demand curve for a product, we were concerned with a single industry. willing to buy as the price of However, a factor input such as skilled labor is demanded by firms in many the product changes. different industries. Moreover, as we move from industry to industry, we are likely to find that firms’ demands for labor (which are derived in part from the demands for the firms’ output) vary substantially. Therefore, to obtain the total market demand for labor curve, we must first determine each industry’s demand for labor, and then add the industry demand curves horizontally. The second step is straightforward. Adding industry demand curves for labor to obtain a market demand curve for labor is just like adding individual product demand curves to obtain the market demand curve for that product. So let’s concentrate our attention on the more difficult first step. DETERMINING INDUSTRY DEMAND The first step—determining industry demand—takes into account the fact that both the level of output produced by the firm and its product price change as the prices of the inputs to production change. It is easiest to determine market demand when there is a single producer. In that case, the marginal revenue product curve is the industry demand curve for the input. When there are many firms, however, the analysis is more com- plex because of the possible interaction among the firms. Consider, for instance, the demand for labor when output markets are perfectly competitive. Then, the marginal revenue product of labor is the product of the price of the good and the marginal product of labor (see equation 14.2), as shown by the curve MRPL1 in Figure 14.5 (a). Suppose initially that the wage rate for labor is $15 per hour and that the firm demands 100 worker-hours of labor. Now the wage rate for this firm falls to $10 per hour. If no other firms could hire workers at the lower wage, then our firm would hire 150 worker-hours of labor (by finding the point on the MRPL1 curve that corresponds to the $10-per-hour wage rate). But if the wage rate falls for all firms in an industry, the industry as a whole will hire more labor. This will
CHAPTER 14 • Markets for Factor Inputs 535 Wage Wage (dollars (dollars per per hour) hour) 15 15 10 MRPL2MRPL1 10 Horizontal Sum If 5 Product Price 5 Unchanged Industry Demand Curve 50 100 120 150 Labor L0 L1 L2 Labor (a) (worker-hours) (b) (worker-hours) FIGURE 14.5 THE INDUSTRY DEMAND FOR LABOR The demand curve for labor of a competitive firm, MRPL1 in (a), takes the product price as given. But as the wage rate falls from $15 to $10 per hour, the product price also falls. Thus the firm’s demand curve shifts down- ward to MRPL2. As a result, the industry demand curve, shown in (b), is more inelastic than the demand curve that would be obtained if the product price were assumed to be unchanged. lead to more output from the industry, a shift to the right of the industry supply curve, and a lower market price for its product. In Figure 14.5 (a), when the product price falls, the original marginal rev- enue product curve shifts downward, from MRPL1 to MRPL2. This shift results in a lower quantity of labor demanded by the firm—120 worker-hours rather than 150. Consequently, industry demand for labor will be lower than it would be if only one firm were able to hire workers at the lower wage. Figure 14.5 (b) illustrates this. The lighter line shows the horizontal sum of the indi- vidual firms’ demands for labor that would result if product price did not change as the wage falls. The darker line shows the industry demand curve for labor, which takes into account the fact that product price will fall as all firms expand their output in response to the lower wage rate. When the wage rate is $15 per hour, industry demand for labor is L0 worker-hours. When it falls to $10 per hour, industry demand increases to L1. Note that this is a smaller increase than L2, which would occur if the product price were fixed. The aggregation of industry demand curves into the market demand curve for labor is the final step: To complete it, we simply add the labor demanded in all industries. The derivation of the market demand curve for labor (or for any other input) is essentially the same when the output market is noncompetitive. The only difference is that it is more difficult to predict the change in product price in response to a change in the wage rate because each firm in the market is likely to be pricing strategically rather than taking price as given.
536 PART 3 • Market Structure and Competitive Strategy EXAMPLE 14.1 THE DEMAND FOR JET FUEL In §2.4, we define the price Jet fuel costs have been highly volatile elasticity of demand as during the past several decades, gen- the percentage change in erally increasing and decreasing in line quantity demanded resulting with oil prices. When fuel prices were from a 1-percent change in high, they made up about 30 percent of the price of a good. airline operating costs, and when they were low, they made up 10 to 15 percent of costs. Overall, jet fuel remains the second-highest expense for airlines (after labor) generally. Understanding the demand for jet fuel is important to managers of oil refineries, who must decide how much jet fuel to produce. It is also crucial to managers of airlines, who must project fuel purchases and costs when fuel prices rise and decide whether to invest in more fuel-efficient planes.2 The effect of the increase in fuel costs on the airline industry depends on the ability of airlines either to cut fuel usage by reducing weight (by carrying less excess fuel) and flying more slowly (reducing drag and increasing engine efficiency) or to pass on their higher costs in customer prices. Thus the price elasticity of demand for jet fuel depends both on the ability to conserve fuel and on the elasticities of demand and supply of travel. To measure the short-run elasticity of demand for jet fuel, we use as the quantity of fuel demanded the number of gallons of fuel used by an airline in all markets within its domestic route network. The price of jet fuel is mea- sured in dollars per gallon. A statistical analysis of demand must control for factors other than price that can explain why some firms demand more fuel than others. Some airlines, for example, use more fuel-efficient jet aircraft than others. A second factor is the length of flights: The shorter the flight, the more fuel consumed per mile of travel. Both of these factors were included in a statistical analysis that relates the quantity of fuel demanded to its price. Table 14.1 shows some short-run price elasticities. (They do not account for the introduction of new types of aircraft.) The jet fuel price elasticities for the airlines range in value from −.06 (for American) to −.15 (for Delta). Overall, the results show that the demand for jet fuel as an input to the production of airline flight-miles is very inelastic. This finding is not surprising: In the short run, there is no good substitute for TABLE 14.1 SHORT-RUN PRICE ELASTICITY OF DEMAND FOR JET FUEL AIRLINE ELASTICITY AIRLINE ELASTICITY American −.06 Delta −.15 Continental −.09 United −.10 2This example is drawn in part from Joseph M. Cigliano, “The Demand for Jet Fuel by the U.S. Domestic Trunk Airlines,” Business Economics (September 1982): 32–36.
CHAPTER 14 • Markets for Factor Inputs 537 Price MRPSR MRPLR FIGURE 14.6 THE SHORT- AND LONG-RUN DEMAND FOR JET FUEL The short-run demand for jet fuel MRPSR is more inelastic than the long-run demand MRPLR. In the short run, airlines cannot reduce fuel consumption much when fuel prices increase. In the long run, however, they can switch to longer, more fuel-efficient routes and put more fuel-efficient planes into service. Quantity of jet fuel jet fuel. The long-run elasticity of demand is higher, however, because air- lines can eventually introduce more energy-efficient airplanes. Figure 14.6 shows the short- and long-run demands for jet fuel. The short- run demand curve, MRPSR, is much less elastic than the long-run demand curve because it takes time to substitute newer, more fuel-efficient airplanes when the price of fuel goes up. The Supply of Inputs to a Firm • average expenditure curve Supply curve When the market for a factor input is perfectly competitive, a firm can purchase representing the price per unit as much of that input as it wants at a fixed market price, which is determined by that a firm pays for a good. the intersection of the market demand and supply curves, as shown in Figure 14.7 (a). The input supply curve facing a firm is then perfectly elastic. Thus, • marginal expenditure in Figure 14.7 (b), a firm is buying fabric at $10 per yard to sew into clothing. curve Curve describing the Because the firm is only a small part of the fabric market, it can buy all it wants additional cost of purchasing without affecting the price. one additional unit of a good. In Section 10.5 we explained that the supply curve AE facing the firm in Figure 14.7 (b) is its average expenditure curve (just as the demand curve facing a firm is its average revenue curve), because it represents the price per unit that the firm pays for the good. On the other hand, the marginal expenditure curve rep- resents the firm’s expenditure on an additional unit that it buys. (The marginal expenditure curve in a factor market is analogous to the marginal revenue curve in the output market.) The marginal expenditure depends on whether you are a competitive buyer or a buyer with monopsony power. If you are a competitive buyer, the cost of each unit is the same no matter how many units you purchase; it is the market price of the good. The price paid is the average expenditure per unit, and the marginal expenditure is equal to the average. Consequently, when the factor market is competitive, the average expenditure and marginal expenditure curves are identical horizontal lines, just as the marginal and aver- age revenue curves are identical (and horizontal) for a competitive firm in the output market.
538 PART 3 • Market Structure and Competitive Strategy Price Price (dollars (dollars per per yard) yard) 10 Market Supply S of Fabric Supply of Market Demand 10 Fabric Facing Firm for Fabric ME = AE D Demand for Fabric MRP 100 Yards of 50 Yards of fabric (b) fabric (a) FIGURE 14.7 A FIRM’S INPUT SUPPLY IN A COMPETITIVE FACTOR MARKET In a competitive factor market, a firm can buy any amount of the input it wants without affecting the price. Therefore, the firm faces a perfectly elastic supply curve for that input. As a result, the quantity of the input purchased by the producer of the product is determined by the intersection of the input demand and supply curves. In (a), the industry quantity demanded and quantity supplied of fabric are equated at a price of $10 per yard. In (b), the firm faces a horizontal marginal expenditure curve at a price of $10 per yard of fabric and chooses to buy 50 yards. How much of the input should a firm facing a competitive factor mar- ket purchase? As long as the marginal revenue product curve lies above the marginal expenditure curve, profit can be increased by purchasing more of the input because the benefit of an additional unit (MRP) exceeds the cost (ME). However, when the marginal revenue product curve lies below the marginal expenditure curve, some units yield benefits that are less than cost. Therefore, profit maximization requires that marginal revenue product be equal to marginal expenditure: ME = MRP (14.5) When we considered the special case of a competitive output market, we saw that the firm bought inputs, such as labor, up to the point at which the marginal revenue product was equal to the price of the input v, as in equation (14.3). In the competitive case, therefore, the condition for profit maximization is that the price of the input be equal to marginal expenditure: ME = w (14.6)
CHAPTER 14 • Markets for Factor Inputs 539 In our example, the price of the fabric ($10 per yard) is determined in the com- petitive fabric market shown in Figure 14.7 (a) at the intersection of the demand and supply curves. Figure 14.7 (b) shows the amount of fabric purchased by a firm at the intersection of the marginal expenditure and marginal revenue prod- uct curves. When 50 yards of fabric are purchased, the marginal expenditure of $10 is equal to the marginal revenue from the sale of clothing made possible by the increased use of fabric in the production process. If less than 50 yards of fabric were purchased, the firm would be forgoing an opportunity to make additional profit from clothing sales. If more than 50 yards were purchased, the cost of the fabric would be greater than the additional revenue from the sale of the extra clothing. The Market Supply of Inputs In §8.6, we explain that the short-run market supply The market supply curve for a factor input is usually upward sloping. We saw curve shows the amount of in Chapter 8 that the market supply for a good sold in a competitive market output that will be produced is usually upward sloping because the marginal cost of producing the good by firms in the market for is typically increasing. This is also the case for fabric and other raw material every possible price. inputs. In §4.2, we explain that an When the input is labor, however, people rather than firms are making sup- increase in the price of a ply decisions. In this case, utility maximization by workers rather than profit good has two effects: The maximization by firms determines supply. In the discussion that follows, we real purchasing power of use the analysis of income and substitution effects from Chapter 4 to show that each consumer decreases although the market supply curve for labor can be upward sloping, it may also, (the income effect) and the as in Figure 14.8, be backward bending. In other words, a higher wage rate can good becomes relatively lead to less labor being supplied. expensive (the substitution effect). To see why a labor supply curve may be backward bending, divide the day into hours of work and hours of leisure. Leisure is a term that describes enjoy- able non-work activities, including sleeping, eating, and household chores. Work benefits the worker only through the income that it generates. We also assume that a worker has the flexibility to choose how many hours per day to work. The wage rate measures the price that the worker places on leisure time, because his or her wage measures the amount of money that the worker gives Wage Supply of Labor (dollars per hour) FIGURE 14.8 BACKWARD-BENDING SUPPLY OF LABOR When the wage rate increases, the hours of work supplied increase initially but can eventually decrease as individuals choose to enjoy more leisure and to work less. The back- ward-bending portion of the labor supply curve arises when the income effect of the higher wage (which encourages more leisure) is greater than the substitution effect (which encourages more work). Hours of work per day
540 PART 3 • Market Structure and Competitive Strategy FIGURE 14.9 720 R w ϭ $30 SUBSTITUTION AND Income INCOME EFFECTS OF (dollars per A WAGE INCREASE day) When the wage rate increases from $10 to $30 per hour, the 240 P B worker’s budget line shifts w ϭ $10 from PQ to RQ. In response, C the worker moves from A to B A while decreasing work hours from 8 to 5. The reduction in Q hours worked arises because the income effect outweighs the substitution effect. In this case, the supply of labor curve is backward bending. 12 16 19 24 Hours of leisure Substitution Effect Income Effect up to enjoy leisure. As the wage rate increases, therefore, the price of leisure also increases. This price change brings about both a substitution effect (a change in relative price with utility held constant) and an income effect (a change in util- ity with relative prices unchanged). There is a substitution effect because the higher price of leisure encourages workers to substitute work for leisure. An income effect occurs because the higher wage rate increases the worker’s pur- chasing power. With higher income, the worker can buy more of many goods, one of which is leisure. If more leisure was chosen, it is because the income effect has encouraged the worker to work fewer hours. Income effects can be large because wages are the primary component of most people’s income. When the income effect outweighs the substitution effect, the result is a backward- bending supply curve. Figure 14.9 illustrates how a backward-bending supply curve for labor can result from the work–leisure decision for a typical weekday. The horizontal axis shows hours of leisure per day, the vertical axis income generated by work. (We assume there are no other sources of income.) Initially the wage rate is $10 per hour, and the budget line is given by PQ. Point P, for example, shows that if an individual worked a 24-hour day he would earn an income of $240. The worker maximizes utility by choosing point A, thus enjoying 16 hours of leisure per day (with 8 hours of work) and earning $80. When the wage rate increases to $30 per hour, the budget line rotates about the horizontal intercept to line RQ. (Only 24 hours of leisure are possible.) Now the worker maximizes utility at B by choosing 19 hours of leisure per day (with 5 hours of work), while earning $150. If only the substitution effect came into play, the higher wage rate would encourage the worker to work 12 hours (at C) instead of 8.
CHAPTER 14 • Markets for Factor Inputs 541 However, the income effect works in the opposite direction. It overcomes the substitution effect and lowers the work day from 8 hours to 5. In real life, a backward-bending labor supply curve might apply to a college student working during the summer to earn living expenses for the school year. As soon as a target level of earnings is reached, the student stops working and allocates more time to leisure. An increase in the wage rate will then lead to fewer hours worked because it enables the student to reach the target level of earnings more quickly. The backward-bending supply curve also applies to taxi drivers. As we saw in Example 5.9, for taxi drivers who have a daily targeted earnings goal, an increase in the hourly wage will reduce the number of hours that the drivers work. E X A M P L E 1 4 . 2 LABOR SUPPLY FOR ONE- AND TWO-EARNER HOUSEHOLDS One of the most dramatic changes in the labor mar- in 397 families.3 One way to describe the work ket in the twentieth century has been the increase decisions of the various family groups is to cal- in women’s participation in the labor force. Whereas culate labor supply elasticities. Each elasticity only 34 percent of women had entered the labor relates the numbers of hours worked not only to force in 1950, the number had risen to just under the wage earned by the head of the household, 60 percent by 2010. Married women account for a but also to the wage of the other member of substantial portion of this increase. The increased two-earner households. Table 14.2 summarizes role of women in the labor market has also had a the results. major impact on housing markets: Where to live and work has increasingly become a joint husband- When a higher wage rate leads to fewer hours and-wife decision. worked, the labor supply curve is backward bend- ing: The income effect, which encourages more The complex nature of the work choice was leisure, outweighs the substitution effect, which analyzed in a study that compared the work encourages more work. The elasticity of labor decisions of 94 unmarried females with the work supply is then negative. Table 14.2 shows that heads decisions of heads of households and spouses of one-earner families with children and two-earner TABLE 14.2 ELASTICITIES OF LABOR SUPPLY (HOURS WORKED) GROUP HEAD’S HOURS SPOUSE’S HOURS HEAD’S HOURS WITH RESPECT TO WITH RESPECT TO WITH RESPECT TO SPOUSE’S WAGE SPOUSE’S WAGE HEAD’S WAGE Unmarried males, no children .026 −.086 −.004 Unmarried females, children .106 −.028 −.059 Unmarried females, no children .011 One-earner family, children −.078 One-earner family, no children .007 Two-earner family, children −.002 Two-earner family, no children −.107 3See Janet E. Kohlhase, “Labor Supply and Housing Demand for One- and Two-Earner Households,” Review of Economics and Statistics 68 (1986): 48–56; and Ray C. Fair and Diane J. Macunovich, “Explaining the Labor Force Participation of Women 20–24” (unpublished, February 1997).
542 PART 3 • Market Structure and Competitive Strategy families (with or without children) all have backward- of .106 associated with single women with chil- bending labor supply curves, with elasticities rang- dren. Married women (listed as spouses of heads ing from −.002 to −.078. Most single-earner heads of households) are also on the backward-bending of households are on the upward-sloping portion portion of the labor supply curve, with elasticities of of the labor supply curve, with the largest elasticity −.028 and −.086. 14.2 Equilibrium in a Competitive Factor Market In §9.2, we explain that in A competitive factor market is in equilibrium when the price of the input equates a perfectly competitive mar- the quantity demanded to the quantity supplied. Figure 14.10 (a) shows such ket, efficiency is achieved an equilibrium for a labor market. At point A, the equilibrium wage rate is wC because the sum of aggre- and the equilibrium quantity supplied is LC. Because they are well informed, all gate consumer and producer workers receive the identical wage and generate the identical marginal revenue surplus is maximized. product of labor wherever they are employed. If any worker had a wage lower than her marginal product, a firm would find it profitable to offer that worker a In §8.7, we explain that higher wage. economic rent is the amount that firms are willing to If the output market is also perfectly competitive, the demand curve for an pay for an input less the input measures the benefit that consumers of the product place on the addi- minimum amount necessary tional use of the input in the production process. The wage rate also reflects the to buy it. cost to the firm and to society of using an additional unit of the input. Thus, at A in Figure 14.10 (a), the marginal benefit of an hour of labor (its marginal revenue product MRPL) is equal to its marginal cost (the wage rate w). When output and input markets are both perfectly competitive, resources are used efficiently because the difference between total benefits and total costs is maximized. Efficiency requires that the additional revenue generated by employing an additional unit of labor (the marginal revenue product of labor, MRPL) equal the benefit to consumers of the additional output, which is given by the price of the product times the marginal product of labor, (P)(MPL). When the output market is not perfectly competitive, the condition MRPL = (P)(MPL) no longer holds. Note in Figure 14.10 (b) that the curve repre- senting the product price multiplied by the marginal product of labor [(P)(MPL)] lies above the marginal revenue product curve [(MR)(MPL)]. Point B is the equi- librium wage wM and the equilibrium labor supply LM. But because the price of the product is a measure of the value to consumers of each additional unit of output that they buy, (P)(MPL) is the value that consumers place on additional units of labor. Therefore, when LM laborers are employed, the marginal cost to the firm wM is less than the marginal benefit to consumers vM. Although the firm is maximizing its profit, its output is below the efficient level and it uses less than the efficient level of the input. Economic efficiency would be increased if more laborers were hired and, consequently, more output produced. (The gains to consumers would outweigh the firm’s lost profit.) Economic Rent The concept of economic rent helps explain how factor markets work. When discussing output markets in the long run in Chapter 8, we defined economic rent as the payments received by a firm over and above the minimum cost
CHAPTER 14 • Markets for Factor Inputs 543 Competitive Output Market Monopolistic Output Market Wage Wage vM SL SL wM B wC A P · MPL DL = MRPL DL = MRPL LC Number of workers LM Number of workers (a) (b) FIGURE 14.10 LABOR MARKET EQUILIBRIUM In a competitive labor market in which the output market is competitive, the equilibrium wage wc is given by the intersection of the demand for labor (marginal revenue product) curve and the sup- ply of labor curve. This is point A in part (a) of the figure. Part (b) shows that when the producer has monopoly power, the marginal value of a worker vM is greater than the wage wM. Thus too few workers are employed. (Point B determines the quantity of labor that the firm hires and the wage rate paid.) of producing its output. For a factor market, economic rent is the difference between the payments made to a factor of production and the minimum amount that must be spent to obtain the use of that factor. Figure 14.11 illustrates the concept of economic rent as applied to a competitive labor market. The equilibrium Wage A SL FIGURE 14.11 Economic Rent DL ϭ MRPL ECONOMIC RENT w* Number of workers The economic rent associated with the employ- B ment of labor is the excess of wages paid above the minimum amount needed to hire workers. The equilibrium wage is given by A, at the inter- section of the labor supply and labor demand curves. Because the supply curve is upward slop- ing, some workers would have accepted jobs for a wage less than w*. The green-shaded area ABw* is the economic rent received by all workers. 0 L*
544 PART 3 • Market Structure and Competitive Strategy price of labor is w*, and the quantity of labor supplied is L*. The supply of labor curve is the upward-sloping curve, and the demand for labor is the downward-sloping marginal revenue product curve. Because the sup- ply curve tells us how much labor will be supplied at each wage rate, the minimum expenditure needed to employ L* units of labor is given by the tan-shaded area AL*0B, below the supply curve to the left of the equilibrium labor supply L*. In perfectly competitive markets, all workers are paid the wage w*. This wage is required to get the last “marginal” worker to supply his or her labor, but all other workers earn rents because their wage is greater than the wage that would be needed to get them to work. Because total wage payments are equal to the rectangle 0w*AL*, the economic rent earned by labor is given by the area ABw*. Note that if the supply curve were perfectly elastic, economic rent would be zero. There are rents only when supply is somewhat inelastic. And when supply is perfectly inelastic, all payments to a factor of production are economic rents because the factor will be supplied no matter what price is paid. As Figure 14.12 shows, one example of an inelastically supplied factor is land. The supply curve is perfectly inelastic because land for housing (or for agriculture) is fixed, at least in the short run. With land inelastically supplied, its price is determined entirely by demand. The demand for land is given by D1, and its price per unit is s1. Total land rent is given by the green-shaded rect- angle. But when the demand for land increases to D2, the rental value per unit of land increases to s2; in this case, total land rent includes the blue-shaded area as well. Thus, an increase in the demand for land (a shift to the right in the demand curve) leads both to a higher price per acre and to a higher economic rent. Price (dollars per acre) FIGURE 14.12 s2 Supply of Land s1 LAND RENT D2 D1 When the supply of land is perfectly inelas- Number of acres tic, the market price of land is determined at the point of intersection with the demand curve. The entire value of the land is then an economic rent. When demand is given by D1, the economic rent per acre is given by s1, and when demand increases to D2, rent per acre increases to s2.
CHAPTER 14 • Markets for Factor Inputs 545 E X A M P L E 1 4 . 3 PAY IN THE MILITARY The U.S. Army had a personnel labor demanded is greater than problem for many years. During the the quantity supplied, and there Civil War, roughly 90 percent of the is a shortage of skilled workers. armed forces were unskilled work- ers involved in ground combat. Over the past decade the mil- Since then, the nature of warfare itary changed its wage structure has evolved. Ground combat forces to maintain an effective fight- now make up less than 20 percent ing force. First, a 2.7 percent of the armed forces. Meanwhile, in pay raise went into effect in the latter half of the 20th century, 2007, followed by a 3.9-percent changes in technology led to shortages in skilled tech- raise in 2009 and a 3.4-percent nicians, trained pilots, computer analysts, mechanics, raise in 2010. Even so, military pay remains low: and others needed to operate sophisticated military As of 2011, a private first-class earned $20,470, a equipment. How did the military respond to this short- sergeant $24,736, a captain $43,927, and a major age? Economics provides some answers. $49,964.4 However, the military went a step further, increasing the number and size of its reenlistment The military pays officers primarily based on years bonuses. Selective reenlistment bonuses were tar- of service. Consequently, officers with differing skill geted at skilled jobs where there were shortages. levels and abilities were usually paid similar salaries. The military also took advantage of the sustained Moreover, some skilled officers were substantially high unemployment rates in the United States from underpaid relative to salaries they could receive 2008 to 2011 by emphasizing the substantial tech- in the private sector. Figure 14.13 shows the inef- nical training that it provided, along with free or ficiency that resulted from this pay policy. The equi- subsidized housing, food, medical care, and educa- librium wage rate w* is the wage that equates the tion. The result of these policies was to move the demand for labor to the supply. With an inflexible market for skilled labor in the military back toward wage structure, the military paid a wage w0, which is the equilibrium market-clear wage w* depicted in below the equilibrium wage. At w0, the quantity of Figure 14.13. Wage SL w* FIGURE 14.13 w0 THE SHORTAGE OF SKILLED Shortage MILITARY PERSONNEL When the wage w* is paid to military per- sonnel, the labor market is in equilibrium. When the wage is kept below w*, at w0, there is a shortage of personnel because the quantity of labor demanded is greater than the quantity supplied. DL = MRPL Number of skilled workers 4http://militarypay.defense.gov/pay
546 PART 3 • Market Structure and Competitive Strategy 14.3 Factor Markets with Monopsony Power In §10.5, we explain that a In some factor markets, individual buyers have buyer power that allows them buyer has monopsony power to affect the prices they pay. Often this happens either when one firm is a mon- when his purchasing deci- opsony buyer or there are only a few buyers, in which case each firm has some sion can affect the price of monopsony power. For example, we saw in Chapter 10 that automobile com- the product. panies have monopsony power as buyers of parts and components. GM and Toyota, for example, buy large quantities of brakes, radiators, and other parts and can negotiate lower prices than those charged smaller purchasers. In other cases, there might be only two or three sellers of a factor and a dozen or more buyers, but each buyer nonetheless has bargaining power—it can negotiate low prices because it makes large and infrequent purchases and can play the sellers off against each other when bargaining over price. Throughout this section, we will assume that the output market is perfectly competitive. In addition, because a single buyer is easier to visualize than sev- eral buyers who all have some monopsony power, we will restrict our attention at first to pure monopsony. In §10.5, we explain that Monopsony Power: Marginal and Average Expenditure marginal expenditure is the cost of one more unit, and When you are deciding how much of a good to purchase, you keep increasing average expenditure is the the number of units purchased until the additional value from the last unit pur- average price paid per unit. chased—the marginal value—is just equal to the cost of that unit—the marginal expenditure. In perfect competition, the price that you pay for the good—the average expenditure—is equal to the marginal expenditure. However, when you have monopsony power, the marginal expenditure is greater than the average expenditure, as Figure 14.14 shows. Price 20 Marginal (per unit Expenditure (ME) FIGURE 14.14 of input) C SL ϭ Average MARGINAL AND AVERAGE 15 Expenditure (AE) EXPENDITURE wC w* ϭ 13 D ϭ MRPL ϭ MV When the buyer of an input has monopsony power, the marginal expenditure curve lies 10 above the average expenditure curve because the decision to buy an extra unit raises the price 5 that must be paid for all units, not just for the last one. The number of units of input purchased is given by L*, at the intersection of the marginal revenue product and marginal expenditure curves. The corresponding wage rate w* is lower than the competitive wage wc. 1 23 4 56 Units of input L* LC
CHAPTER 14 • Markets for Factor Inputs 547 The factor supply curve facing the monopsonist is the market supply curve, which shows how much of the factor suppliers are willing to sell as its price increases. Because the monopsonist pays the same price for each unit, the supply curve is its average expenditure curve. The average expenditure curve is upward sloping because the decision to buy an extra unit raises the price that must be paid for all units, not just the last one. For a profit-maximizing firm, however, the marginal expenditure curve is relevant in deciding how much to buy. The mar- ginal expenditure curve lies above the average expenditure curve: When the firm increases the price of the factor to hire more units, it must pay all units that higher price, not just the last unit hired. Purchasing Decisions with Monopsony Power How much of the input should the firm buy? As we saw earlier, it should buy up to the point where marginal expenditure equals marginal revenue product. Here the benefit from the last unit bought (MRP) is just equal to the cost (ME). Figure 14.14 illustrates this principle for a labor market. Note that the monop- sonist hires L* units of labor; at that point, ME = MRPL. The wage rate w* that workers are paid is given by finding the point on the average expenditure or supply curve with L* units of labor. As we showed in Chapter 10, a buyer with monopsony power maximizes net benefit (utility less expenditure) from a purchase by buying up to the point where marginal value (MV) is equal to marginal expenditure: MV = ME For a firm buying a factor input, MV is just the marginal revenue product of the factor MRP. Thus, we have (as in the case of a competitive factor market) ME = MRP (14.7) Note from Figure 14.14 that the monopsonist hires less labor than a firm or group of firms with no monopsony power. In a competitive labor market, LC workers would be hired: At that level, the quantity of labor demanded (given by the marginal revenue product curve) is equal to the quantity of labor supplied (given by the average expenditure curve). Note also that the monopsonistic firm will be paying its workers a wage w* that is less than the wage wC that would be paid in a competitive market. Monopsony power can arise in different ways. One source can be the special- ized nature of a firm’s business. If the firm buys a component that no one else buys, it is likely to be a monopsonist in the market for that component. Another source can be a business’s location—it may be the only major employer within an area. Monopsony power can also arise when the buyers of a factor form a car- tel to limit purchases of the factor, in order to buy it at less than the competitive price. (But as we explained in Chapter 10, this is a violation of the antitrust laws.) Few firms in our economy are pure monopsonists. But many firms (or indi- viduals) have some monopsony power because their purchases account for a large portion of the market. The government is a monopsonist when it hires vol- unteer soldiers or buys missiles, aircraft, and other specialized military equip- ment. A mining firm or other company that is the only major employer in a community also has monopsony power in the local labor market. Even in these
548 PART 3 • Market Structure and Competitive Strategy cases, however, monopsony power may be limited because the government competes to some extent with other firms that offer similar jobs. Likewise, the mining firm competes to some extent with companies in nearby communities. Bargaining Power In some factor markets, there are a small number of sellers and a small number of buyers. In such cases, an individual buyer and an individual seller will nego- tiate with each other to determine a price. The resulting price might be high or low, depending on which side has more bargaining power. The amount of bargaining power that a buyer or seller has is determined in part by the number of competing buyers and competing sellers. But it is also determined by the nature of the purchase itself. If each buyer makes large and infrequent purchases, it can sometimes play the sellers off against each other when negotiating a price and thereby amass considerable bargaining power. An example of this kind of bargaining power occurs in the market for commer- cial aircraft. Airplanes are clearly key factor inputs for airlines, and airlines want to buy planes at the lowest possible prices. There are dozens of airlines, however, and only two major producers of commercial aircraft—Boeing and Airbus. One might think that as a result, Boeing and Airbus would have a considerable advantage when negotiating prices. The opposite is true. It is important to understand why. Airlines do not buy planes every day, and they do not usually buy one plane at a time. A company like American Airlines will typically order new planes only every three or four years, and each order might be for 20 or 30 planes, at a cost of several billion dollars. As big as Boeing and Airbus are, this is no small purchase, and each seller will do all it can to win the order. American Airlines knows this and can use it to its advantage. If, for example, American is choosing between 20 new Boeing 787s or 20 new Airbus A380s (which are similar airplanes), it can play the two companies off against each other when negotiating a price. Thus if Boeing offers a price of, say, $300 million per plane, American might go to Airbus and ask it to do better. Whatever Airbus offers, American will then go back to Boeing and demand a bigger discount, claiming (truthfully or otherwise) that Airbus is offer- ing large discounts. Then back to Airbus, back to Boeing, and so on, until American has succeeded in obtaining a large discount from one of the two companies. EXAMPLE 14.4 MONOPSONY POWER IN THE MARKET FOR BASEBALL PLAYERS In the United States, major ate a monopsonistic cartel. Like league baseball is exempt from all cartels, this one depended the antitrust laws, the result of a on an agreement among own- Supreme Court decision and the ers. The agreement involved policy of Congress not to apply an annual draft of players and those laws to labor markets.5 This a reserve clause that effectively exemption allowed baseball team tied each player to one team owners (before 1975) to oper- for life, thereby eliminating 5This example builds on an analysis of the structure of baseball players’ salaries by Roger Noll, who has kindly supplied us with the relevant data.
CHAPTER 14 • Markets for Factor Inputs 549 most interteam competition for players. Once a agents after playing for a team for six years. The player was drafted by a team, he could not play reserve clause was no longer in effect, and a highly for another team unless rights were sold to that monopsonistic labor market became much more team. As a result, baseball owners had monopsony competitive. power in negotiating new contracts with their play- ers: The only alternative to signing an agreement The result was an interesting experiment in labor was to give up the game or play it outside the market economics. Between 1975 and 1980, the United States. market for baseball players adjusted to a new post– reserve clause equilibrium. Before 1975, expendi- During the 1960s and early 1970s, baseball tures on players’ contracts made up approximately players’ salaries were far below the market value 25 percent of all team expenditures. By 1980, of their marginal products (determined in part by those expenditures had increased to 40 percent. the incremental attention that better hitting or Moreover, the average player’s salary doubled in pitching might achieve). For example, if the play- real terms. By 1992, the average baseball player ers’ market had been perfectly competitive, those was earning $1,014,942—a very large increase players receiving a salary of about $42,000 in 1969 from the monopsonistic wages of the 1960s. In would have instead received a salary of $300,000 1969, for example, the average baseball salary was in 1969 dollars (which is $1.7 million in year 2007 approximately $42,000 adjusted for inflation, about dollars). $236,000 in year 2007 dollars. Fortunately for the players, and unfortunately for Salaries for baseball players continued to grow. the owners, there was a strike in 1972 followed by Whereas the average salary was just less than a lawsuit by one player (Curt Flood of the St. Louis $600,000 in 1990, it had risen to $1,998,000 in 2000 Cardinals) and an arbitrated labor–management and $3,305,393 by 2011, and many players earned agreement. This process eventually led in 1975 to much more. The New York Yankees as a team aver- an agreement by which players could become free aged $8,947,937 in 2011. E X A M P L E 1 4 . 5 TEENAGE LABOR MARKETS AND THE MINIMUM WAGE Increases in the national mini- increased.6 A study of the effects mum wage rate (which was $4.50 of the minimum wage on employ- in early 1996 and $7.20 in 2011) ment in fast-food restaurants in were controversial, raising the New Jersey added to that contro- question of whether the cost of versy.7 any unemployment that might be generated would be outweighed Some states have minimum by the benefit of higher incomes wages above the Federal level. to those whose wages have been In April 1992 the New Jersey minimum wage was increased 6See Example 1.4 (page 15) for an initial discussion of the minimum wage, and Section 9.3 (page 328) for an analysis of its effects on employment. 7David Card and Alan Krueger, “Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania,” American Economic Review 84 (September 1994). See also David Card and Alan B. Krueger, “A Reanalysis of the Effect of the New Jersey Minimum Wage on the Fast-Food Industry with Representative Payroll Data,” Working Paper No. 6386, Cambridge, MA: National Bureau of Economic Research, 1998; and Madeline Zavodny, “Why Minimum Wage Hikes May Not Reduce Employment,” Federal Reserve Bank of Atlanta, Economic Review, Second Quarter, 1998.
550 PART 3 • Market Structure and Competitive Strategy from $4.25 to $5.05 per hour. Using a survey wage, but would also increase the employment of 410 fast-food restaurants, David Card and level (from L* to LC). Alan Krueger found that employment had actu- ally increased by 13 percent after the minimum Does the fast-food study show that employ- wage went up. What is the explanation for this ers have monopsony power in this labor market? surprising result? One possibility is that restau- The evidence suggests no. If firms do have mon- rants responded to the higher minimum wage by opsony power but the fast-food market is com- reducing fringe benefits, which usually take the petitive, then the increase in the minimum wage form of free and reduced-price meals for employ- should have no effect on the price of fast food. ees. A related explanation is that employers Because the market for fast food is so competi- responded by providing less on-the-job training tive, firms paying the higher minimum wage would and by lowering the wages for those with experi- be forced to absorb the higher wage cost them- ence who had previously been paid more than the selves. The study suggests, however, that prices new minimum wage. did increase after the introduction of the higher minimum wage. An alternative explanation for the increased New Jersey employment holds that the labor The Card-Krueger analysis of the minimum market for teenage (and other) unskilled work- wage remains hotly debated. A number of crit- ers is not highly competitive. If so, the analysis ics argued that the New Jersey study was atypi- of Chapter 9 does not apply. If the unskilled fast- cal. Others questioned the reliability of the data, food labor market were monopsonistic, for exam- arguing that a higher minimum wage reduces ple, we would expect a different effect from the employment (see our discussion in Chapter 9).8 In increased minimum wage. Suppose that the wage response, Card and Krueger repeated their study, of $4.25 was the wage that fast-food employers using a more comprehensive and accurate data with monopsony power in the labor market would set. They obtained the same results. Where does offer their workers even if there were no minimum this leave us? Perhaps a better characterization of wage. Suppose also that $5.10 would be the wage low-wage labor markets requires a more sophisti- enjoyed by workers if the labor market were fully cated theory (e.g., the efficiency wage theory dis- competitive. As Figure 14.14 shows, the increase cussed in Chapter 17). In any case, new empirical in the minimum wage would not only raise the analyses should shed more light on the effects of the minimum wage. In §9.3, we explain that set- 14.4 Factor Markets with Monopoly Power ting a minimum wage in a perfectly competitive market Just as buyers of inputs can have monopsony power, sellers of inputs can can create unemployment have monopoly power. In the extreme, the seller of an input may be a and a deadweight loss. monopolist, as when a firm has a patent to produce a computer chip that no other firm can duplicate. Because the most important example of monop- In §10.2, we explain that a oly power in factor markets involves labor unions, we will concentrate seller of a product has some most of our attention there. In the subsections that follow, we show how a monopoly power if it can labor union, which is a monopolist in the sale of labor services, might profitably charge a price increase the well-being of its members and substantially affect nonunionized greater than marginal cost. workers. 8For example, see Donald Deere, Kevin M. Murply, and Finis Welch, “Employment and the 1990– 1991 Minimum Wage Hike,” American Economic Review, Papers and Proceedings 85 (May 1995): 232–37; and David Neumark and William Wascher, “Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania: Comment,” American Economic Review 90 (2000): 1362–96.
CHAPTER 14 • Markets for Factor Inputs 551 Wage SL FIGURE 14.15 per A MONOPOLY POWER OF SELLERS OF LABOR worker When a labor union is a monopolist, it chooses among w1 points on the buyer’s demand for labor curve DL. The seller can maximize the number of workers hired, at w2 L*, by agreeing that workers will work at wage w*. The quantity of labor L1 that maximizes the rent earned by w* employees is determined by the intersection of the marginal revenue and supply of labor curves; union DL members will receive a wage rate of w1. Finally, if the MR union wishes to maximize total wages paid to workers, it should allow L2 union members to be employed at a wage rate of w2. At that point, the marginal revenue to the union will be zero. L 1 L2 L* Number of workers Monopoly Power over the Wage Rate In §7.1, we explain that opportunity cost is the cost Figure 14.15 shows a demand for labor curve in a market with no monopsony associated with opportuni- power: It aggregates the marginal revenue products of firms that compete to ties that are foregone by not buy labor. The labor supply curve describes how union members would supply putting a firm’s resources to labor if the union exerted no monopoly power. In that case, the labor market their best alternative use. would be competitive, and L* workers would be hired at a wage of w*, where demand DL equals supply SL. Because of its monopoly power, however, the union can choose any wage rate and the corresponding quantity of labor supplied, just as a monopolist seller of output chooses price and the corresponding quantity of output. If the union wanted to maximize the number of workers hired, it would choose the com- petitive outcome at A. However, if the union wished to obtain a higher-than- competitive wage, it could restrict its membership to L1 workers. As a result, the firm would pay a wage rate of w1. Although union members who work would be better off, those who cannot find jobs would be worse off. Is a policy of restrictive union membership worthwhile? If the union wishes to maximize the economic rent that its workers receive, the answer is yes. By restricting membership, the union would be acting like a monopolist, which restricts output in order to maximize profit. To a firm, profit is the revenue that it receives less its opportunity costs. To a union, rent represents the wages that its members earn as a group in excess of their opportunity cost. To maximize rent, the union must choose the number of workers hired so that the marginal revenue to the union (the additional wages earned) is equal to the extra cost of inducing workers to work. This cost is a marginal opportunity cost because it is a measure of what an employer has to offer an additional worker to get him or her to work for the firm. However, the wage that is necessary to encourage addi- tional workers to take jobs is given by the supply of labor curve SL. The rent-maximizing combination of wage rate and number of workers is given by the intersection of the MR and SL curves. We have chosen the wage-employment combination of w1 and L1 with the rent-maximization premise in mind. The shaded area below the demand for labor curve, above the supply of labor curve and to the left of L1, represents the economic rent that all workers receive.
552 PART 3 • Market Structure and Competitive Strategy A rent-maximizing policy might benefit nonunion workers if they can find non- union jobs. However, if these jobs are not available, rent maximization could cre- ate too sharp a distinction between winners and losers. An alternative objective is to maximize the aggregate wages that all union members receive. Look again at the example in Figure 14.15. To achieve this goal, the number of workers hired is increased from L1 until the marginal revenue to the union is equal to zero. Because any further employment decreases total wage payments, aggregate wages are maximized when the wage is equal to w2 and the number of workers is equal to L2. Unionized and Nonunionized Workers When the union uses its monopoly power to increase members’ wages, fewer unionized workers are hired. Because these workers either move to the non- union sector or choose initially not to join the union, it is important to under- stand what happens in the nonunionized part of the economy. Assume that the total supply of unionized and nonunionized workers is fixed. In Figure 14.16, the market supply of labor in both sectors is given by SL. The demand for labor by firms in the unionized sector is given by DU, the demand in the nonunionized sector by DNU. Total market demand is the hori- zontal sum of the demands in the two sectors and is given by DL. Suppose the union chooses to increase the wage rate of its workers above the competitive wage w*, to wU. At that wage rate, the number of workers hired in the unionized sector falls by an amount ⌬LU, as shown on the horizontal axis. As these workers find employment in the nonunionized sector, the wage rate in that sector adjusts until the labor market is in equilibrium. At the new wage rate in the nonunionized sector, wNU, the additional number of workers hired in that sector, ⌬LNU, is equal to the number of workers who left the unionized sector. Figure 14.16 shows an adverse consequence of a union strategy directed toward raising union wages: Nonunionized wages fall. Unionization can improve working conditions and provide useful information to workers and management. But when the demand for labor is not perfectly inelastic, union workers are helped at the expense of nonunion workers. Wage SL per FIGURE 14.16 worker WAGE DISCRIMINATION IN UNIONIZED AND NONUNIONIZED SECTORS wU w* When a monopolistic union raises the wage in the unionized wNU sector of the economy from w* to wU, employment in that sector falls, as shown by the movement along the demand curve DU. DU DNU DL For the total supply of labor, given by SL, to remain unchanged, the wage in the nonunionized sector must fall from w* to wNU, as Number of shown by the movement along the demand curve DNU. workers ΔLU ΔLNU
CHAPTER 14 • Markets for Factor Inputs 553 E X A M P L E 1 4 . 6 THE DECLINE OF PRIVATE-SECTOR UNIONISM For several decades, the membership of labor between union and nonunion wages decreased unions has been declining. Figure 14.7 shows the substantially as unions focused on employment decline in union membership over the past thirty rather than wages. In the 1980s in response to years. The decline has been relatively steady, but union demands, the pattern evolved further as as we moved into the 21st century the rate of employers put into place two-tiered wage provi- decline began to diminish and it has stabilized in sions in which wages for experienced workers were recent years at about 12 percent. Interestingly, kept high, but newer union members were paid on this 12 percent average masks huge differences a lower wage scale. between the public sector, where unionization was 36.2 percent in 2010, and the private sector, where During the past two decades, a number of eco- unionization was only 6.9%. nomic forces have led to a further narrowing of the union-nonunion wage differential, which has How have unions responded to this impor- remained constant over the past ten years.9 Why tant dynamic? We might expect that the decline did the wage differential decline over time? For in union bargaining power might lead to differ- one thing, the demand for unionized employees ent responses by union negotiators, and this has has become increasingly elastic over time as firms indeed been the case. Historically, union wages have found it easier to substitute capital for skilled have been higher than the wages of their nonunion labor in the production process. For another, global- counterparts. During the 1970s, the differential ization has meant that many companies were able Percent 24 22 20 18 16 14 12 10 Year 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 FIGURE 14.17 UNION WORKERS AS A PERCENTAGE OF TOTAL The percentage of workers that are unionized has been declining steadily over the past 30 years. Data from U.S. Bureau of Labor Statistics. 9According to the Bureau of Labor Statistics, in 2010, the average union worker in the private sector earned $23.19 per hour in wage and salary income, while the average nonunion worker earned $19.28 per hour.
554 PART 3 • Market Structure and Competitive Strategy to organize their production processes so as to hire on wages in order to maintain employment levels. nonunion labor, either within or outside the United Under substantial competitive pressure, they have States. Faced with an elastic demand for its services, agreed to maintain a two-tier wage and benefits unions would have little choice but to give ground structure. E X A M P L E 1 4 . 7 WAGE INEQUALITY REVISITED In Example 2.2, we explained how of education is summarized in the rapid growth in the demand Figure 14.18, which shows (for for skilled relative to unskilled 2010) median weekly earnings— labor has been partly responsi- as well as unemployment rates— ble for the growing inequality in for different levels of education. the distribution of income in the Education clearly pays. Workers United States. As we explained, with more education not only while the demand for skilled labor receive higher salaries, but they has steadily increased, the sup- are also much less likely to lose ply of skilled labor has not grown their jobs and become unem- much. Instead, it has been the supply of unskilled ployed in an economic downturn. For example, in labor that has grown. What are the reasons for these 2010 the average unemployment rate was 5.4% for changes in relative demand and supply? Have the those with a bachelor’s degree, and 14.9% for those decline in private-sector unionism and the failure of who had not completed high school. the minimum wage to keep up with inflation been A clue to what happened is given by the important factors? Or is it the increasing importance dramatic increase in the use of computers by of education, along with the role that computers workers. In 1984, 25 percent of all workers used now play in the labor market? A recent study pro- computers; that figure is now close to 60 percent, vides some answers.10 and it is over 80 percent for managers and pro- fessionals.12 Education and computer use have From 1980 through the present, college gradu- gone hand in hand to increase the demand for ates’ relative wages have grown. This is not consis- skilled workers. A statistical analysis shows that, tent with what one would expect if the decline of overall, the spread of computer technology is unionism and/or changes in the minimum wage responsible for nearly half the increase in relative was the primary reason for the growing inequality. wages. Furthermore, the growth in the demand In 1963 the hourly wage of a typical college gradu- for skilled workers has occurred primarily within ate was 1.5 times that of a high school graduate. By industries where computers have become 2009, that ratio had increased to 1.95. By 2010, the increasingly useful. median weekly salary of those with a college degree These data, along with the numbers shown in (but no further education) was $1038, whereas those Figure 14.18, should motivate you to continue your with a high-school degree earned only $626. Moving college and graduate studies—especially your study beyond college to a further professional degree of microeconomics. led to a median wage of $1610.11 The importance 10David Autor, “The Polarization of Job Opportunities in the U.S. Labor Market,” Center for American Progress: The Hamilton Project, April, 2010. See also David H. Autor, Lawrence Katz, and Alan B. Krueger, “Computing Inequality: Have Computers Changed the Labor Market?” Quarterly Journal of Economics 113 (November 1998): 1169–1213. 11Bureau of Labor Statistics, Current Population Survey 2010. 12National Center for Educational Statistics, Digest of Educational Statistics, Table 432.
CHAPTER 14 • Markets for Factor Inputs 555 Unemployment rate in 2010 (%) Median weekly earnings in 2010 ($) 1.9 Doctoral degree 1,550 2.4 Professional degree 1,610 4.0 Master’s degree 1,272 5.4 Bachelor’s degree 1,038 7.0 Associate degree 767 9.2 712 10.3 Some college, 626 14.9 no degree 444 Average: 8.2% Average: $782 High school diploma Less than a high school diploma FIGURE 14.18 EDUCATION, EARNINGS, AND EMPLOYMENT Median weekly earnings (in 2010) were much higher, and average unemployment rates were much lower, for workers with higher levels of education. Data from U.S. Bureau of Labor Statistics, Current Population Survey. SUMMARY 5. The market supply of a factor such as labor need not be upward sloping. A backward-bending labor supply 1. In a competitive input market, the demand for an curve can result if the income effect associated with a input is given by the marginal revenue product, the higher wage rate (more leisure is demanded because product of the firm’s marginal revenue, and the mar- it is a normal good) is greater than the substitution ginal product of the input. effect (less leisure is demanded because its price has gone up). 2. A firm in a competitive labor market will hire workers to the point at which the marginal revenue product of 6. Economic rent is the difference between the payments labor is equal to the wage rate. This principle is analo- to factors of production and the minimum payment gous to the profit-maximizing output condition that that would be needed to employ them. In a labor mar- production be increased to the point at which marginal ket, rent is measured by the area below the wage level revenue is equal to marginal cost. and above the marginal expenditure curve. 3. The market demand for an input is the horizontal 7. When a buyer of an input has monopsony power, sum of industry demands for the input. But industry the marginal expenditure curve lies above the aver- demand is not the horizontal sum of the demands of age expenditure curve, which reflects the fact that the all the firms in the industry. To determine industry monopsonist must pay a higher price to attract more demand, one must remember that the market price of of the input into employment. the product will change in response to changes in the price of an input. 8. When the input seller is a monopolist, such as a labor union, the seller chooses the point on the marginal 4. When factor markets are competitive, the buyer of an revenue product curve that best suits its objective. input assumes that its purchases will have no effect on Maximization of employment, economic rent, and its price. As a result, the firm’s marginal expenditure wages are three plausible objectives for labor unions. and average expenditure curves are both perfectly elastic.
556 PART 3 • Market Structure and Competitive Strategy QUESTIONS FOR REVIEW experienced football players if the draft system were repealed and all teams could compete for college 1. Why is a firm’s demand for labor curve more inelastic players? when the firm has monopoly power in the output mar- 9. The government wants to encourage individuals on ket than when the firm is producing competitively? welfare to become employed. It is considering two possible incentive programs: 2. Why might a labor supply curve be backward bending? a. Give firms $2 per hour for every individual on wel- 3. How is a computer company’s demand for computer fare who is hired. programmers a derived demand? b. Give each firm that hires one or more welfare work- 4. Compare the hiring choices of a monopsonistic and ers a payment of $1000 per year, irrespective of the a competitive employer of workers. Which will hire number of hires. more workers, and which will pay the higher wage? To what extent is each of these programs likely to be Explain. effective at increasing the employment opportunities 5. Rock musicians sometimes earn several million dollars for welfare workers? per year. Can you explain such large incomes in terms 10. A small specialty cookie company, whose only vari- of economic rent? able input is labor, finds that the average worker can 6. What happens to the demand for one input when the produce 50 cookies per day, the cost of the average use of a complementary input increases? worker is $64 per day, and the price of a cookie is $1. Is 7. For a monopsonist, what is the relationship between the company maximizing its profit? Explain. the supply of an input and the marginal expenditure 11. A firm uses both labor and machines in production. on it? Explain why an increase in the average wage rate 8. Currently the National Football League has a system causes both a movement along the labor demand for drafting college players by which each player is curve and a shift of the curve. picked by only one team. The player must sign with that team or not play in the league. What would hap- pen to the wages of both newly drafted and more EXERCISES d. Suppose that the price of the product remains at $2 and the wage at $16, but that there is a techno- 1. Suppose that the wage rate is $16 per hour and the logical breakthrough that increases output by 25 price of the product is $2. Values for output and labor percent for any given level of labor. Find the new are in units per hour. profit-maximizing L. qL 2. Assume that workers whose incomes are less than $10,000 currently pay no federal income taxes. Suppose 00 a new government program guarantees each worker 20 1 $5000, whether or not he or she earns any income. 35 2 For all earned income up to $10,000, the worker must 47 3 pay a 50-percent tax. Draw the budget line facing the 57 4 worker under this new program. How is the program 65 5 likely to affect the labor supply curve of workers? 70 6 3. Using your knowledge of marginal revenue product, a. Find the profit-maximizing quantity of labor. explain the following: b. Suppose that the price of the product remains at a. A famous tennis star is paid $200,000 for appear- ing in a 30-second television commercial. The actor $2 but that the wage rate increases to $21. Find the who plays his doubles partner is paid $500. new profit-maximizing level of L. b. The president of an ailing savings and loan is paid c. Suppose that the price of the product increases to not to stay in his job for the last two years of his $3 and the wage remains at $16 per hour. Find the contract. new profit-maximizing L. c. A jumbo jet carrying 400 passengers is priced higher than a 250-passenger model even though both aircraft cost the same to manufacture.
CHAPTER 14 • Markets for Factor Inputs 557 4. The demands for the factors of production listed below 8. The demand for labor by an industry is given by the have increased. What can you conclude about changes curve L = 1200 − 10w, where L is the labor demanded in the demands for the related consumer goods? If per day and w is the wage rate. The supply curve is demands for the consumer goods remain unchanged, given by L = 20w. What is the equilibrium wage rate what other explanation is there for an increase in and quantity of labor hired? What is the economic rent derived demands for these items? earned by workers? a. Computer memory chips b. Jet fuel for passenger planes 9. Using the same information as in Exercise 8, suppose c. Paper used for newsprint now that the only labor available is controlled by a d. Aluminum used for beverage cans monopolistic labor union that wishes to maximize the rent earned by union members. What will be the quan- 5. Suppose there are two groups of workers, union- tity of labor employed and the wage rate? How does ized and nonunionized. Congress passes a law that your answer compare with your answer to Exercise 8? requires all workers to join the union. What do you Discuss. (Hint: The union’s marginal revenue curve is expect to happen to the wage rates of formerly non- given by MR = 120 − 0.2L.) unionized workers? Of those workers who were origi- nally unionized? What have you assumed about the *10. A firm uses a single input, labor, to produce output q union’s behavior? according to the production function q = 8 1L. The commodity sells for $150 per unit and the wage rate is 6. Suppose that a firm’s production function is given by $75 per hour. Q = 12L − L2, for L = 0 to 6, where L is labor input a. Find the profit-maximizing quantity of L. per day and Q is output per day. Derive and draw b. Find the profit-maximizing quantity of q. the firm’s demand for labor curve if the firm’s out- c. What is the maximum profit? put sells for $10 in a competitive market. How many d. Suppose now that the firm is taxed $30 per unit of workers will the firm hire when the wage rate is $30 output and that the wage rate is subsidized at a per day? $60 per day? (Hint: The marginal product of rate of $15 per hour. Assume that the firm is a price labor is 12 − 2L.) taker, so the price of the product remains at $150. Find the new profit-maximizing levels of L, q, and 7. The only legal employer of military soldiers in the profit. United States is the federal government. If the govern- e. Now suppose that the firm is required to pay a 20 ment uses its knowledge of its monopsonistic position, percent tax on its profits. Find the new profit-maxi- what criteria will it employ when determining how mizing levels of L, q, and profit. many soldiers to recruit? What happens if a manda- tory draft is implemented?
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C H A P T E R 15 Investment, Time, and Capital Markets CHAPTER OUTLINE 15.1 Stocks versus Flows 560 In Chapter 14, we saw that in competitive markets, firms decide 15.2 Present Discounted 561 how much to purchase each month by comparing the marginal Value revenue product of each factor to its cost. The decisions of all firms determine the market demand for each factor, and the market price is 15.3 The Value of a Bond 564 the price that equates the quantity demanded with the quantity sup- plied. For factor inputs such as labor and raw materials, this picture is 15.4 The Net Present Value 569 reasonably complete, but not so for capital. The reason is that capital Criterion for Capital is durable: It can last and contribute to production for years after it is Investment Decisions purchased. 15.5 Adjustments for Risk 573 Firms sometimes rent capital in much the same way that they hire workers. For example, a firm might rent office space for a monthly fee, 15.6 Investment Decisions 578 just as it hires a worker for a monthly wage. But more often, capital by Consumers expenditures involve the purchases of factories and equipment that are expected to last for years. This introduces the element of time. When a 15.7 Investments in Human firm decides whether to build a factory or purchase machines, it must compare the outlays it would have to make now with the additional Capital 580 profit that the new capital will generate in the future. To make this com- parison, it must address the following question: How much are future *15.8 Intertemporal Production profits worth today? This problem does not arise when hiring labor or purchasing raw materials. To make those choices, the firm need only Decisions—Depletable compare its current expenditure on the factor—e.g., the wage or the price of steel—with the factor’s current marginal revenue product. Resources 584 In this chapter, we will learn how to calculate the current value 15.9 How Are Interest Rates of future flows of money. This is the basis for our study of the firm’s investment decisions. Most of these decisions involve comparing an Determined? 588 outlay today with profits that will be received in the future; we will see how firms can make this comparison and determine whether the LIST OF EXAMPLES outlay is warranted. Often, the future profits resulting from a capital investment are higher or lower than anticipated. We will see how firms 15.1 The Value of Lost 563 can take this kind of uncertainty into account. Earnings Individuals also make decisions involving costs and benefits occur- 15.2 The Yields on Corporate ring at different points in time, and the same principles apply. For example, we will see how a consumer choosing a new air conditioner Bonds 567 can determine whether it makes economic sense to buy a more energy- efficient model that costs more but will result in lower electricity bills 15.3 The Value of a New York in the future. We will also discuss investments in human capital. Does it make economic sense, for example, to go to college or graduate school City Taxi Medallion 573 rather than take a job and start earning an income? 15.4 Capital Investment in the Disposable Diaper Industry 576 15.5 Choosing an Air 579 Conditioner and a New Car 15.6 Should You Go to 582 Business School? 15.7 How Depletable Are Depletable Resources? 587 559
560 PART 3 • Market Structure and Competitive Strategy In §14.1, we explain that in We will examine other intertemporal decisions that firms sometimes face. For a competitive factor market, example, producing a depletable resource, such as natural gas or oil, means that the demand for each fac- less will be available to produce in the future. How should a producer take this tor is given by its marginal into account? How long should a timber company let trees grow before harvest- revenue product—i.e., the ing them for lumber? additional revenue earned from an incremental unit of The answers to these investment and production decisions depend in the factor. part on the interest rate that one pays or receives when borrowing or lending money. We will discuss the factors that determine interest rates and explain why interest rates on government bonds, corporate bonds, and savings accounts differ. Recall from §6.1 that a firm’s 15.1 Stocks versus Flows production function involves flows of inputs and outputs: Before proceeding, we must be clear about how to measure capital and It turns certain amounts of other factor inputs that firms purchase. Capital is measured as a stock, i.e., labor and capital each year as a quantity of plant and equipment that the firm owns. For example, if a into an amount of output firm owns an electric motor factory worth $10 million, we say that it has that same year. a capital stock worth $10 million. Inputs of labor and raw materials, on the other hand, are measured as flows. The output of the firm is also a flow. For example, this same firm might use 20,000 worker-hours of labor and 20,000 pounds of copper per month to produce 8000 electric motors per month. (The choice of monthly units is arbitrary; we could just as well have expressed these quantities in weekly or annual terms—for example, 240,000 worker- hours of labor per year, 240,000 pounds of copper per year, and 96,000 motors per year.) Let’s look at this producer of electric motors in more detail. Both variable cost and the rate of output are flows. Suppose the wage rate is $15 per hour and the price of copper is $2.00 per pound. Thus the variable cost is (20,000)($15) + (20,000)($2.00) = $340,000 per month. Average variable cost, on the other hand, is a cost per unit: $340,000 per month 8000 units per month = $42.50 per unit Suppose the firm sells its motors for $52.50 each. Then its average profit is $52.50 - $42.50 = $10.00 per unit, and its total profit is $80,000 per month. (Note that total profit is also a flow.) To make and sell these motors, how- ever, the firm needs capital—namely, the factory that it built for $10 million. Thus the firm’s $10 million capital stock allows it to earn a flow of profit of $80,000 per month. Was the $10 million investment in this factory a sound decision? To answer this question, we must translate the $80,000 per month profit flow into a number that we can compare with the factory’s $10 million cost. Suppose the factory is expected to last for 20 years. In that case the problem, simply put, is: What is the value today of $80,000 per month for the next 20 years? If that value is greater than $10 million, the investment was a good one. A profit of $80,000 per month for 20 years comes to ($80,000)(20)(12) = $19.2 million. That would make the factory seem like an excellent investment. But is $80,000 five years—or 20 years—from now worth $80,000 today? No, because money today can be invested—in a bank account, a bond, or other interest-bearing
CHAPTER 15 • Investment, Time, and Capital Markets 561 assets—to yield more money in the future. As a result, $19.2 million received over the next 20 years is worth less than $19.2 million today. 15.2 Present Discounted Value We will return to our $10 million electric motor factory in Section 15.4, but first • interest rate Rate at which we must address a basic problem: How much is $1 paid in the future worth today? one can borrow or lend money. The answer depends on the interest rate: the rate at which one can borrow or lend money. • present discounted value (PDV) The current value of an Suppose the annual interest rate is R. (Don’t worry about which interest rate expected future cash flow. this actually is; later, we’ll discuss the various types of interest rates.) Then $1 today can be invested to yield (1 + R) dollars a year from now. Therefore, 1 + R dollars is the future value of $1 today. Now, what is the value today, i.e., the present discounted value (PDV), of $1 paid one year from now? The answer is easy: because 1 + R dollars one year from now is worth (1 + R)/(1 + R) = $1 today, $1 a year from now is worth $1/(1 + R) today. This is the amount of money that will yield $1 after one year if invested at the rate R. What is the value today of $1 paid two years from now? If $1 were invested today at the interest rate R, it would be worth 1 + R dollars after one year, and (1 + R)(1 + R) = (1 + R)2 dollars at the end of two years. Because (1 + R)2 dollars two years from now is worth $1 today, $1 two years from now is worth $1/(1 + R)2 today. Similarly, $1 paid three years from now is worth $1/(1 + R)3 today, and $1 paid n years from now is worth $1/(1 + R)n today.1 We can summarize this as follows: PDV of $1 paid after 1 year = $1 (1 + R) PDV of $1 paid after 2 years = $1 (1 + R)2 PDV of $1 paid after 3 years = $1 (1 + R)3 f PDV of $1 paid after n years = $1 (1 + R)n Table 15.1 shows, for different interest rates, the present value of $1 paid after 1, 2, 5, 10, 20, and 30 years. Note that for interest rates above 6 or 7 percent, $1 paid 20 or 30 years from now is worth very little today. But this is not the case for low interest rates. For example, if R is 3 percent, the PDV of $1 paid 20 years from now is about 55 cents. In other words, if 55 cents were invested now at the rate of 3 percent, it would yield about $1 after 20 years. 1We are assuming that the annual rate of interest R is constant from year to year. Suppose the annual interest rate were expected to change, so that R1 is the rate in year 1, R2 is the rate in year 2, and so forth. After two years, $1 invested today would be worth (1 + R1)(1 + R2), so that the PDV of $1 received two years from now is $1/(1 + R1)(1 + R2). Similarly, the PDV of $1 paid n years from now is $1/(1 + R1)(1 + R2)(1 + R3)…(1 + Rn).
562 PART 3 • Market Structure and Competitive Strategy TABLE 15.1 PDV OF $1 PAID IN THE FUTURE INTEREST 1 YEAR 2 YEARS 5 YEARS 10 YEARS 20 YEARS 30 YEARS RATE $0.990 $0.980 $0.951 $0.905 $0.820 $0.742 0.01 0.980 0.961 0.906 0.820 0.673 0.552 0.02 0.971 0.943 0.863 0.744 0.554 0.412 0.03 0.962 0.925 0.822 0.676 0.456 0.308 0.04 0.952 0.907 0.784 0.614 0.377 0.231 0.05 0.943 0.890 0.747 0.558 0.312 0.174 0.06 0.935 0.873 0.713 0.508 0.258 0.131 0.07 0.926 0.857 0.681 0.463 0.215 0.099 0.08 0.917 0.842 0.650 0.422 0.178 0.075 0.09 0.909 0.826 0.621 0.386 0.149 0.057 0.10 0.870 0.756 0.497 0.247 0.061 0.015 0.15 0.833 0.694 0.402 0.162 0.026 0.004 0.20 Valuing Payment Streams We can now determine the present value of a stream of payments over time. For example, consider the two payment streams in Table 15.2. Stream A comes to $200: $100 paid now and $100 a year from now. Stream B comes to $220: $20 paid now, $100 a year from now, and $100 two years from now. Which payment stream would you prefer to receive? The answer depends on the interest rate. To calculate the present discounted value of these two streams, we compute and add the present values of each year’s payment: PDV of Stream A = $100 + $100 (1 + R) PDV of Stream B = $20 + $100 + $100 (1 + R) (1 + R)2 Table 15.3 shows the present values of the two streams for interest rates of 5, 10, 15, and 20 percent. As the table shows, the preferred stream depends on the interest rate. For interest rates of 10 percent or less, Stream B is worth more; for interest rates of 15 percent or more, Stream A is worth more. Why? Because even though less is paid out in Stream A, it is paid out sooner. TABLE 15.2 TWO PAYMENT STREAMS Payment Stream A: TODAY 1 YEAR 2 YEARS Payment Stream B: $100 $100 $0 $ 20 $100 $100
CHAPTER 15 • Investment, Time, and Capital Markets 563 TABLE 15.3 PDV OF PAYMENT STREAMS PDV of Stream A: R ؍.05 R ؍.10 R ؍.15 R ؍.20 PDV of Stream B: $195.24 $190.91 $186.96 $183.33 205.94 193.55 182.57 172.78 This simple example shown in Tables 15.2 and 15.3 illustrates an important principle. The present value of a stream of payments depends on three things: (1) the amount of each payment, (2) the timing of the payments, and (3) the interest rate used to discount payments made in the future. As we will see, this principle applies to a wide variety of problems. E X A M P L E 1 5 . 1 THE VALUE OF LOST EARNINGS In legal cases involving accidents, victims or their heirs (if the victim is killed) sue the injuring party (or an insurance company) to recover damages. In addition to compensating for pain and suffering, those damages include the future income that the injured or deceased person would have earned had the accident not occurred. To see how the present value of lost earnings can be calculated, let’s examine an actual 1996 accident case. (The names and some of the data have been changed to preserve anonymity.) Harold Jennings died in an automobile accident on January 1, 1996, at the age of 53. His family sued the driver of the other car for negligence. A major part of the damages they asked to be awarded was the present value of the earnings that Jennings would have received from his job as an airline pilot had he not been killed. The calculation of present value is typical of cases like this. Had he worked in 1996, Jennings’ salary would have been $85,000. The normal age of retirement for an airline pilot is 60. To calculate the present value of Jennings’ lost earnings, we must take several things into account. First, Jennings’ salary would probably have increased over the years. Second, we cannot be sure that he would have lived to retirement had the accident not occurred; he might have died from some other cause. Therefore, the PDV of his lost earnings until retirement at the end of 2003 is PDV = W0 + W0(1 + g)(1 - m1) + W0(1 + g)2(1 - m2) (1 + R) (1 + R)2 + g + W0(1 + g)7(1 - m7) (1 + R)7 where W0 is his salary in 1996, g is the annual percentage rate at which his salary is likely to have grown (so that W0(1 + g) would be his salary in 1997, W0(1 + g)2 his salary in 1998, etc.), and m1, m2,…, m7 are mortality rates, i.e.,
564 PART 3 • Market Structure and Competitive Strategy TABLE 15.4 CALCULATING LOST WAGES YEAR W0(1 + g)t (1 – mt) 1/(1 + R)t W0(1 + g)t (1 – mt)/(1 + R)t 1996 $ 85,000 .991 1.000 $84,235 1997 91,800 .990 .917 83,339 1998 99,144 .989 .842 82,561 1999 .988 .772 81,671 2000 107,076 .987 .708 80,810 2001 115,642 .986 .650 80,044 2002 124,893 .985 .596 79,185 2003 134,884 .984 .547 78,409 145,675 the probabilities that he would have died from some other cause by 1997, 1998,…, 2003. To calculate this PDV, we need to know the mortality rates m1,…, m7, the expected rate of growth of Jennings’ salary g, and the interest rate R. Mortality data are available from insurance tables that provide death rates for men of similar age and race.2 As a value for g, we can use 8 percent, the average rate of growth of wages for airline pilots over the period 1985–1995. Finally, for the interest rate we can use the rate on govern- ment bonds, which at the time was about 9 percent. (We will say more about how one chooses the correct interest rate to discount future cash flows in Sections 15.4 and 15.5.) Table 15.4 shows the details of the pres- ent value calculation. By summing the last column, we obtain a PDV of $650,254. If Jennings’ family was successful in proving that the defendant was at fault, and if there were no other damage issues involved in the case, they could recover this amount as compensation.3 15.3 The Value of a Bond • bond Contract in which A bond is a contract in which a borrower agrees to pay the bondholder (the a borrower agrees to pay the lender) a stream of money. For example, a corporate bond (a bond issued by bondholder (the lender) a stream a corporation) might make “coupon” payments of $100 per year for the next of money. ten years, and then a principal payment of $1000 at the end of the ten-year period.4 How much would you pay for such a bond? To find out how much 2Mortality data can be found in the Statistical Abstract of the United States (Table 105 in the 2011 Edition). 3Actually, this sum should be reduced by the amount of Jennings’ wages which would have been spent on his own consumption and which would not therefore have benefited his wife or children. 4In the United States, the coupon payments on most corporate bonds are made in semiannual install- ments. To keep the arithmetic simple, we will assume that they are made annually.
CHAPTER 15 • Investment, Time, and Capital Markets 565 PDV of 2.0 cash flow 1.9 (thousands of dollars) 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.05 0.10 0.15 0.20 0 Interest rate FIGURE 15.1 PRESENT VALUE OF THE CASH FLOW FROM A BOND Because most of the bond’s payments occur in the future, the present discounted value declines as the interest rate increases. For example, if the interest rate is 5 percent, the PDV of a 10-year bond paying $100 per year on a principal of $1000 is $1386. At an interest rate of 15 percent, the PDV is $749. the bond is worth, we simply compute the present value of the payment stream: PDV = $100 + $100 + g + $100 + $1000 (15.1) (1 + R) (1 + R)2 (1 + R)10 (1 + R)10 Again, the present value depends on the interest rate. Figure 15.1 shows the value of the bond—the present value of its payment stream—for interest rates up to 20 percent. Note that the higher the interest rate, the lower the value of the bond. At an interest rate of 5 percent, the bond is worth about $1386, but at an interest rate of 15 percent, its value is only $749. Perpetuities • perpetuity Bond paying out a fixed amount of money each A perpetuity is a bond that pays out a fixed amount of money each year, forever. year, forever. How much is a perpetuity that pays $100 per year worth? The present value of the payment stream is given by the infinite summation: PDV = $100 + $100 + $100 + $100 +g (1 + R) (1 + R)2 (1 + R)3 (1 + R)4
566 PART 3 • Market Structure and Competitive Strategy Fortunately, it isn’t necessary to calculate and add up all these terms to find the value of this perpetuity; the summation can be expressed in terms of a sim- ple formula.5 PDV = $100/R (15.2) So if the interest rate is 5 percent, the perpetuity is worth $100/(.05) = $2000, but if the interest rate is 20 percent, the perpetuity is worth only $500. The Effective Yield on a Bond Many corporate and most government bonds are traded on the bond market. The value of a traded bond can be determined directly by looking at its market price—the value placed on it by buyers and sellers.6 Thus we usually know the value of a bond, but to compare the bond with other investment opportunities, we would like to determine the interest rate consistent with that value. • effective yield (or rate of EFFECTIVE YIELD Equations (15.1) and (15.2) show how the values of two return) Percentage return that different bonds depend on the interest rate used to discount future payments. one receives by investing in a These equations can be “turned around” to relate the interest rate to the bond’s bond. value. This is particularly easy to do for the perpetuity. Suppose the market price—and thus the value—of the perpetuity is P. Then from equation (15.2), P = $100/R, and R = $100/P. Thus, if the price of the perpetuity is $1000, we know that the interest rate is R = $100/$1000 = 0.10, or 10 percent. This interest rate is called the effective yield, or rate of return: the percentage return that one receives by investing in a bond. For the ten-year coupon bond in equation (15.1), calculating the effective yield is a bit more complicated. If the price of the bond is P, we write equation (15.1) as P= $100 + $100 + $100 + g + $100 + $1000 (1 + R) (1 + R)2 (1 + R)3 (1 + R)10 (1 + R)10 Given the price P, this equation must be solved for R. Although there is no simple formula to express R in terms of P in this case, there are methods (sometimes available on calculators and spreadsheet programs such as Excel) for calculating R numerically. Figure 15.2, which plots the same curve as that in Figure 15.1, shows how R depends on P for this ten-year coupon bond. Note that if the price of the bond is $1000, the effective yield is 10 percent. If the price rises to $1300, the effective yield drops to about 6 percent. If the price falls to $700, the effective yield rises to over 16 percent. Yields can differ considerably among different bonds. Corporate bonds gen- erally yield more than government bonds, and as Example 15.2 shows, the bonds of some corporations yield much more than the bonds of others. One of the most important reasons for this is that different bonds carry different degrees of risk. The U.S. government is less likely to default (fail to make interest or principal 5Let x be the PDV of $1 per year in perpetuity, so x = 1/(1 + R) + 1/(1 + R)2 + …. Then x(1 + R) = 1 + 1/(1 + R) + 1/(1 + R)2 + …, so x(1 + R) = 1 + x, xR = 1, and x = 1/R. 6The prices of actively traded corporate and U.S. government bonds are shown on financial market Web sites such as www.yahoo.com, www.bloomberg.com, and www.schwab.com.
CHAPTER 15 • Investment, Time, and Capital Markets 567 PDV of 2.0 payments 1.9 (value of bond) 1.8 (thousands 1.7 of dollars) 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.05 0.10 0.15 0.20 0 Interest rate FIGURE 15.2 EFFECTIVE YIELD ON A BOND The effective yield is the interest rate that equates the present value of the bond’s payment stream with the bond’s market price. The figure shows the pres- ent value of the payment stream as a function of the interest rate. The effective yield is found by drawing a horizontal line at the level of the bond’s price. For example, if the price of this bond were $1000, its effective yield would be 10 percent. If the price were $1300, the effective yield would be about 6 percent; if the price were $700, it would be 16.2 percent. payments) on its bonds than is a private corporation. And some corporations are financially stronger and therefore less likely to default than others. As we saw in Chapter 5, the more risky an investment, the greater the return that an investor demands. As a result, riskier bonds have higher yields. E X A M P L E 1 5 . 2 THE YIELDS ON CORPORATE BONDS To see how corporate bond yields are calculated—and how they can dif- fer from one corporation to another—let’s examine the yields for two cou- pon bonds: one issued by Microsoft and the other by the drug store chain Rite Aid. Each has a face value of $100, which means that when the bond matures, the holder receives a principal payment of that amount. Each bond makes a “coupon” (i.e., interest) payment every six months.7 7These bonds actually have a face value of $1000, not $100. The prices and coupon payments are listed as though the face value were $100; to get the actual prices and payments, just multiply by 10 the numbers that appear on financial Web sites or in the newspaper.
568 PART 3 • Market Structure and Competitive Strategy We calculate the bond yields using the closing prices on August 1, 2011. The following information was downloaded from the Yahoo! Finance Web site: Price ($): Microsoft Rite Aid Coupon ($): 106.60 93.00 Maturity Date: 5.300 9.500 Yield to Maturity (%): Feb. 8, 2041 Jun. 15, 2017 Current Yield (%): 4.877 11.099 Rating: 4.972 10.215 AAA CCC What do these numbers mean? For Microsoft, the price of $106.60 was the closing price on August 1, 2011, based on a face value for the bond of $100. The coupon of $5.30 means that $2.65 is paid to the owner of the bond every six months. The maturity date is the date at which the bond comes due and the owner receives the $100 face value. The 4.877 percent yield to maturity, discussed further below, is the effective yield (i.e., rate of return) on the bond. The current yield is simply the cou- pon divided by the price, i.e., 5.300/106.60 = 4.972 percent. (The current yield is of limited relevance because it doesn’t tell us the actual rate of return on the bond.) Finally, the Microsoft bond is rated AAA, which is the highest rating possible for a corporate bond, indicating that the likeli- hood of default is very low. How does one determine the effective yield (i.e., rate of return, or yield to maturity) on this bond? For simplicity, we’ll assume that the coupon pay- ments are made annually instead of every six months. (The error that this introduces is small.) Because the Microsoft bond matures in 2041, coupon payments will be made for 2041 – 2011 = 30 years. Thus the yield is given by the following equation: 106.60 = 5.3 + 5.3 + 5.3 +g+ 5.3 + 5.3 (1 + R) (1 + R)2 (1 + R)3 (1 + R )29 (1 + R)30 To find the effective yield, we must solve this equation for R.8 You can check (by substituting to see whether the equation is satisfied) that the solution is approximately R* = 4.877 percent. The effective yield on the Rite Aid bond is found the same way. The bond had a price of $93.00, made coupon payments of $9.50 per year, and had 2017 – 2011 = 6 years to mature. Thus the equation for its yield is: 93.00 = 9.5 + 9.5 + 9.5 + 9.5 + 9.5 + 9.5 (1 + R) (1 + R)2 (1 + R)3 (1 + R)4 (1 + R)5 (1 + R)6 8Solving the equation for R can be done in Excel by using Solver.
CHAPTER 15 • Investment, Time, and Capital Markets 569 The solution to this equation is R* = 11.099 percent. Why was the yield on the Rite Aid bond so much higher than on the Microsoft bond? Because the Rite Aid bond was much riskier. By 2011, the drug store chain was suffering large losses due to increasing competition from larger chains like Wal-Mart, which were able to use their scale to undercut prices on everything from toiletries to prescription drugs. Between 2007 and 2011, Rite Aid turned a profit for only one quarter, leading many analysts to predict bank- ruptcy. Consistent with this, Rite Aid’s bond was rated CCC (the lowest rank- ing). Because investors knew that there was a significant possibility that Rite Aid would default on its bond payments, they were prepared to buy the bond only if the expected return was high enough to compensate them for the risk. 15.4 The Net Present Value Criterion for Capital Investment Decisions One of the most common and important decisions that firms make is to invest In §7.1, we explain that a in new capital. Millions of dollars may be invested in a factory or machines sunk cost is an expenditure that will last—and affect profits—for many years. The future cash flows that that has been made and the investment will generate are often uncertain. And once the factory has been cannot be recovered. built, the firm usually cannot disassemble and resell it to recoup its invest- ment—it becomes a sunk cost. • net present value (NPV) criterion Rule holding that one How should a firm decide whether a particular capital investment is worth- should invest if the present value while? It should calculate the present value of the future cash flows that it expects of the expected future cash flow to receive from the investment and compare it with the cost of the investment. from an investment is larger than This method is known as the net present value (NPV) criterion: the cost of the investment. NPV criterion: Invest if the present value of the expected future cash flows from an investment is larger than the cost of the investment. Suppose a capital investment costs C and is expected to generate profits over the next 10 years of amounts p1, p2,…, p10. We then write the net present value as NPV = -C + p1 + p2 +g+ p10 (15.3) (1 + R) (1 + R)2 (1 + R)10 where R is the discount rate that we use to discount the future stream of prof- • discount rate Rate used to its. (R might be a market interest rate or some other rate; we will discuss how determine the value today of a to choose it shortly.) Equation (15.3) describes the net benefit to the firm from dollar received in the future. the investment. The firm should make the investment only if that net benefit is positive—i.e., only if NPV > 0. DETERMINING THE DISCOUNT RATE What discount rate should the firm use? The answer depends on the alternative ways that the firm could use its money. For example, instead of this investment, the firm might invest
570 PART 3 • Market Structure and Competitive Strategy • opportunity cost of in another piece of capital that generates a different stream of profits. Or it capital Rate of return that one might invest in a bond that yields a different return. As a result, we can think could earn by investing in an of R as the firm’s opportunity cost of capital. Had the firm not invested in alternate project with similar risk. this project, it could have earned a return by investing in something else. The correct value for R is therefore the return that the firm could earn on a “similar” investment. By “similar” investment, we mean one with the same risk. As we saw in Chapter 5, the more risky an investment, the greater the return one expects to receive from it. Therefore, the opportunity cost of investing in this proj- ect is the return that one could earn from another project or asset of similar riskiness. We’ll see how to evaluate the riskiness of an investment in the next sec- tion. For now, let’s assume that this project has no risk (i.e., the firm is sure that the future profit flows will be p1, p2, etc.). In that case, the opportunity cost of the investment is the risk-free return—e.g., the return one could earn on a government bond. If the project is expected to last for 10 years, the firm could use the annual interest rate on a 10-year government bond to com- pute the NPV of the project, as in equation (15.3).9 If the NPV is zero, the benefit from the investment would just equal the opportunity cost, so the firm should be indifferent between investing and not investing. If the NPV is greater than zero, the benefit exceeds the opportunity cost, so the investment should be made.10 The Electric Motor Factory In Section 15.1, we discussed a decision to invest $10 million in a factory to pro- duce electric motors. This factory would enable the firm to use labor and cop- per to produce 8000 motors per month for 20 years at a cost of $42.50 each. The motors could be sold for $52.50 each, for a profit of $10 per unit, or $80,000 per month. We will assume that after 20 years, the factory will be obsolete but can be sold for scrap for $1 million. Is this a good investment? To find out, we must calculate its net present value. We will assume for now that the $42.50 production cost and the $52.50 price at which the motors can be sold are certain, so that the firm is sure that it will receive $80,000 per month, or $960,000 per year, in profit. We also assume that the $1 million scrap value of the factory is certain. The firm should therefore use a risk-free interest rate to discount future profits. Writing the cash flows in mil- lions of dollars, the NPV is NPV = - 10 + .96 + .96 + .96 (15.4) (1 + R) (1 + R)2 (1 + R)3 + c + .96 + 1 (1 + R)20 (1 + R)20 9This is an approximation. To be precise, the firm should use the rate on a one-year bond to discount p1, the rate on a two-year bond to discount p2, etc. 10This NPV rule is incorrect when the investment is irreversible, subject to uncertainty, and can be delayed. For a treatment of irreversible investment, see Avinash Dixit and Robert Pindyck, Investment under Uncertainty (Princeton, NJ: Princeton University Press, 1994).
CHAPTER 15 • Investment, Time, and Capital Markets 571 Net 10 present 9 value (millions 8 of dollars) 7 FIGURE 15.3 6 NET PRESENT VALUE OF A FACTORY 5 The NPV of a factory is the pres- 4 ent discounted value of all the cash flows involved in build- 3 ing and operating it. Here it is the PDV of the flow of future 2 profits less the current cost of construction. The NPV declines 1 as the discount rate increases. At discount rate R*, the NPV is 0 zero. –1 –2 –3 –4 –5 –6 0 0.05 R* 0.10 0.15 0.20 Discount rate, R Figure 15.3 shows the NPV as a function of the discount rate R. Note that at the rate R*, which is about 7.5 percent, the NPV is equal to zero. (The rate R* is sometimes referred to as the internal rate of return on the investment.) For discount rates below 7.5 percent, the NPV is positive, so the firm should invest in the factory. For discount rates above 7.5 percent, the NPV is negative, and the firm should not invest. Real versus Nominal Discount Rates In the example above, we assumed that future cash flows are certain, so that the discount rate R should be a risk-free interest rate, such as the rate on U.S. gov- ernment bonds. Suppose that rate happened to be 9 percent. Does that mean the NPV is negative and the firm should not invest? To answer this question, we must distinguish between real and nominal dis- count rates, and between real and nominal cash flows. Let’s begin with the cash flows. In Chapter 1, we discussed real versus nominal prices. We explained that whereas the real price is net of inflation, the nominal price includes infla- tion. In our example, we assumed that the electric motors coming out of our factory could be sold for $52.50 each over the next 20 years. We said nothing, however, about the effect of inflation. Is the $52.50 a real price, i.e., net of infla- tion, or does it include inflation? As we will see, the answer to this question can be critical. Let’s assume that the $52.50 price—and the $42.50 production cost—are in real terms. This means that if we expect a 5-percent annual rate of infla- tion, the nominal price of the motors will increase from $52.50 in the first year to (1.05)(52.50) = $55.13 in the second year, to (1.05)(55.13) = $57.88 in the third year, and so on. Therefore, our profit of $960,000 per year is also in real terms.
572 PART 3 • Market Structure and Competitive Strategy Opportunity cost is dis- Now let’s turn to the discount rate. If the cash flows are in real terms, the discount cussed in §7.1. rate must also be in real terms. Why? Because the discount rate is the opportunity cost of the investment. If inflation is not included in the cash flows, it should not be included in the opportunity cost either. In our example, the discount rate should therefore be the real interest rate on government bonds. The nominal interest rate (9 percent) is the rate that we see in the newspapers; it includes inflation. The real interest rate is the nominal rate minus the expected rate of inflation.11 If we expect inflation to be 5 percent per year on average, the real interest rate would be 9 - 5 = 4 percent. This is the discount rate that should be used to calculate the NPV of the investment in the electric motor factory. Note from Figure 15.3 that at this rate the NPV is clearly positive, so the investment should be undertaken. When the NPV rule is used to evaluate investments, the numbers in the cal- culations may be in real or in nominal terms, as long as they are consistent. If cash flows are in real terms, the discount rate should also be in real terms. If a nominal discount rate is used, the effect of future inflation must also be included in the cash flows. Negative Future Cash Flows Factories and other production facilities can take several years to build and equip. The cost of the investment will also be spread out over several years, instead of occurring only at the outset. In addition, some investments are expected to result in losses, rather than profits, for the first few years. (For exam- ple, demand may be low until consumers learn about the product, or costs may start high and fall only when managers and workers have moved down the learning curve.) Negative future cash flows create no problem for the NPV rule; they are simply discounted, just like positive cash flows. For example, suppose that our electric motor factory will take a year to build: $5 million is spent right away, and another $5 million is spent next year. Also, suppose the factory is expected to lose $1 million in its first year of operation and $0.5 million in its second year. Afterward, it will earn $0.96 million a year until year 20, when it will be scrapped for $1 million, as before. (All these cash flows are in real terms.) Now the net present value is NPV = -5 - 5 - 1 - .5 + .96 + .96 (1 + R) (1 + R)2 (1 + R)3 (1 + R)4 (1 + R)5 (15.5) +g+ .96 + 1 (1 + R)20 (1 + R)20 Suppose the real interest rate is 4 percent. Should the firm build this fac- tory? You can confirm that the NPV is negative, so this project is not a good investment. 11People may have different views about future inflation and may therefore have different estimates of the real interest rate.
CHAPTER 15 • Investment, Time, and Capital Markets 573 E X A M P L E 1 5 . 3 THE VALUE OF A NEW YORK CITY TAXI MEDALLION We saw in Example 9.5 that in 2011, the number of taxi medallions in New York was roughly the same as in 1937, so that the price of a medallion was $880,000. (Recall that a medallion is a permit allowing a taxicab to be used to transport passengers.) The medallions are owned by taxi companies, which have successfully pressured the city government to limit the number in circulation, thereby maintaining the high price — at the cost of making it difficult for citizens to find a taxi. A taxi medallion allows its owner to lease a cab to a driver and thereby earn a profit from the operation of the cab. Is that profit high enough to justify an $880,000 value for each medallion? To find out, let’s calculate the flow of income a taxi company can expect from leasing a medallion to one or more taxi drivers. The taxi company charges the driver a flat fee for use of the medallion, but that fee is capped by the city. In 2011, the fee was $110 per 12-hour shift, or $220 per day. Assuming the cab is driven 7 days per week and 50 weeks per year, the taxi company would earn (7)(50)($220) = $77,000 per year from the medallion. Little risk is involved (there is a shortage of taxis, so it is easy to find drivers willing to lease the medallion), and the capped fee has increased with inflation. Therefore a 5-percent discount rate would probably be appropriate for discounting future income flows. Assuming a time horizon of 20 years, the present value of this flow of income is therefore: PV = 70,000 + 70,000 + 70,000 + c + 70,000 = $872,355 1.05 1.052 1.053 1.0520 Thus a medallion price in the range of $880,000 is consistent with the flow of income that the medallion will bring to the taxi company. 15.5 Adjustments for Risk We have seen that a risk-free interest rate is an appropriate discount rate for future • risk premium Amount cash flows that are certain. For most projects, however, future cash flows are far from of money that a risk-averse certain. At our electric motor factory, for example, we would expect uncertainty individual will pay to avoid over future copper prices, over the future demand and the price of motors, and even taking a risk. over future wage rates. Thus the firm cannot know what its profits from the factory will be over the next 20 years. Its best estimate of profits might be $960,000 per year, but actual profits may turn out to be higher or lower. How should the firm take this uncertainty into account when calculating the net present value of the project? A common practice is to increase the discount rate by adding a risk premium to the risk-free rate. The idea is that the owners of the firm are risk averse, which makes future cash flows that are risky worth less than those that are certain. Increasing the discount rate takes this into account by reducing the present value of those future cash flows. But how large should the risk premium be? As we will see, the answer depends on the nature of the risk.
574 PART 3 • Market Structure and Competitive Strategy • diversifiable risk Risk that Diversifiable versus Nondiversifiable Risk can be eliminated either by investing in many projects or Adding a risk premium to the discount rate must be done with care. If the firm’s by holding the stocks of many managers are operating in the stockholders’ interests, they must distinguish companies. between two kinds of risk—diversifiable and nondiversifiable.12 Diversifiable risk can be eliminated by investing in many projects or by holding the stocks of many • nondiversifiable risk Risk companies. Nondiversifiable risk cannot be eliminated in this way. Only nondiver- that cannot be eliminated by sifiable risk affects the opportunity cost of capital and should enter into the risk premium. investing in many projects or by holding the stocks of many DIVERSIFIABLE RISK To understand this, recall from Chapter 5 that diversify- companies. ing can eliminate many risks. For example, I cannot know whether the result of a coin flip will be heads or tails. But I can be reasonably sure that out of a thousand coin flips, roughly half will be heads. Similarly, an insurance company that sells me life insurance cannot know how long I will live. But by selling life insurance to thousands of people, it can be reasonably sure about the percentage of those who will die each year. Much the same is true about capital investment decisions. Although the profit flow from a single investment may be very risky, overall risk will be much less if the firm invests in dozens of projects (as most large firms do). Furthermore, even if the company invests in only one project, stockholders can easily diver- sify by holding the stocks of a dozen or more different companies, or by holding a mutual fund that invests in many stocks. Thus, stockholders—the owners of the firm—can eliminate diversifiable risk. Because investors can eliminate diversifiable risk, they cannot expect to earn a return higher than the risk-free rate by bearing it: No one will pay you for bearing a risk that there is no need to bear. And indeed, assets that have only diversifiable risk tend on average to earn a return close to the risk-free rate. Now, remember that the discount rate for a project is the opportunity cost of investing in that project rather than in some other project or asset with similar risk char- acteristics. Therefore, if the project’s only risk is diversifiable, the opportunity cost is the risk-free rate. No risk premium should be added to the discount rate. NONDIVERSIFIABLE RISK What about nondiversifiable risk? First, let’s be clear about how such risk can arise. For a life insurance company, the possibility of a major war poses nondiversifiable risk. Because a war may increase mortal- ity rates sharply, the company cannot expect that an “average” number of its customers will die each year, no matter how many customers it has. As a result, most insurance policies, whether for life, health, or property, do not cover losses resulting from acts of war. For capital investments, nondiversifiable risk arises because a firm’s profits tend to depend on the overall economy. When economic growth is strong, cor- porate profits tend to be higher. (For our electric motor factory, the demand for motors is likely to be strong, so profits increase.) On the other hand, profits tend to fall in a recession. Because future economic growth is uncertain, diversifica- tion cannot eliminate all risk. Investors should (and indeed can) earn higher returns by bearing this risk. To the extent that a project has nondiversifiable risk, the opportunity cost of investing in that project is higher than the risk-free rate. Thus a risk premium 12Diversifiable risk is also called nonsystematic risk and nondiversifiable risk is called systematic risk. Adding a simple risk premium to the discount rate may not always be the correct way of dealing with risk. See, for example, Richard Brealey and Stewart Myers, Principles of Corporate Finance (New York: McGraw-Hill, 2011).
CHAPTER 15 • Investment, Time, and Capital Markets 575 must be included in the discount rate. Let’s see how the size of that risk pre- mium can be determined. The Capital Asset Pricing Model • Capital Asset Pricing Model (CAPM) Model in which The Capital Asset Pricing Model (CAPM) measures the risk premium for a cap- the risk premium for a capital ital investment by comparing the expected return on that investment with the investment depends on the expected return on the entire stock market. To understand the model, suppose, correlation of the investment’s first, that you invest in the entire stock market (say, through a mutual fund). In return with the return on the that case, your investment would be completely diversified and you would bear entire stock market. no diversifiable risk. You would, however, bear nondiversifiable risk because the stock market tends to move with the overall economy. (The stock market reflects expected future profits, which depend in part on the economy.) As a result, the expected return on the stock market is higher than the risk-free rate. Denoting the expected return on the stock market by rm and the risk-free rate by rf, the risk premium on the market is rm - rf. This is the additional expected return you get for bearing the nondiversifiable risk associated with the stock market. Now consider the nondiversifiable risk associated with one asset, such as a com- pany’s stock. We can measure that risk in terms of the extent to which the return on the asset tends to be correlated with (i.e., move in the same direction as) the return on the stock market as a whole. For example, one company’s stock might have almost no correlation with the market as a whole. On average, the price of that stock would move independently of changes in the market, so it would have little or no nondi- versifiable risk. The return on that stock should therefore be about the same as the risk-free rate. Another stock, however, might be highly correlated with the market. Its price changes might even amplify changes in the market as a whole. That stock would have substantial nondiversifiable risk, perhaps more than the stock market as a whole. If so, its return on average will exceed the market return rm. The CAPM summarizes this relationship between expected returns and the risk premium by the following equation: ri - rj = b(rm - rf) (15.6) where ri is the expected return on an asset. The equation says that the risk pre- • asset beta A constant mium on the asset (its expected return less the risk-free rate) is proportional to the that measures the sensitivity risk premium on the market. The constant of proportionality, b, is called the asset of an asset’s return to market beta. It measures the sensitivity of the asset’s return to market movements and, movements and, therefore, the therefore, the asset’s nondiversifiable risk. If a 1-percent rise in the market tends asset’s nondiversifiable risk. to result in a 2-percent rise in the asset price, the beta is 2. If a 1-percent rise in the market tends to result in a 1-percent rise in the asset price, the beta is 1. And if a 1-percent rise in the market tends to result in no change in the price of the asset, the beta is zero. As equation (15.6) shows, the larger the beta, the greater the expected return on the asset. Why? Because the asset’s nondiversifiable risk is greater. THE RISK-ADJUSTED DISCOUNT RATE Given beta, we can determine the cor- rect discount rate to use in computing an asset’s net present value. That discount rate is the expected return on the asset or on another asset with the same risk. It is therefore the risk-free rate plus a risk premium to reflect nondiversifiable risk: Discount rate = rf + b(rm - rf) (15.7)
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